Linear recurrences associated to rays in Pascal’s triangle and combinatorial identities
Abstract Our main purpose is to describe the recurrence relation associated to the sum of diagonal elements laying along a finite ray crossing Pascal’s triangle. We precise the generating function of the sequence of described sums. We also answer a question of Horadam posed in his paper [Chebyshev a...
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Gespeichert in:
| Autor*in: |
Belbachir, Hacène [verfasserIn] |
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| Format: |
Artikel |
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| Erschienen: |
2014 |
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| Schlagwörter: |
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| Anmerkung: |
© 2014 Mathematical Institute, Slovak Academy of Sciences |
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| Übergeordnetes Werk: |
Enthalten in: Mathematica Slovaca - Versita, 1976, 64(2014), 2 vom: 01. Apr., Seite 287-300 |
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| Übergeordnetes Werk: |
volume:64 ; year:2014 ; number:2 ; day:01 ; month:04 ; pages:287-300 |
| Links: |
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| DOI / URN: |
10.2478/s12175-014-0203-0 |
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OLC213639827X |
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| 520 | |a Abstract Our main purpose is to describe the recurrence relation associated to the sum of diagonal elements laying along a finite ray crossing Pascal’s triangle. We precise the generating function of the sequence of described sums. We also answer a question of Horadam posed in his paper [Chebyshev and Pell connections, Fibonacci Quart. 43 (2005), 108–121]. Further, using Morgan-Voyce sequence, we establish the nice identity $F_{n + 1} - iF_n = i^n \sum\limits_{k = 0}^n {(_{2k}^{n + k} )( - 2 - i)^k } $ of Fibonacci numbers, where i is the imaginary unit. Finally, connections to continued fractions, bivariate polynomials and finite differences are given. | ||
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10.2478/s12175-014-0203-0 doi (DE-627)OLC213639827X (DE-B1597)s12175-014-0203-0-p DE-627 ger DE-627 rakwb 510 VZ 510 VZ 17,1 ssgn Belbachir, Hacène verfasserin aut Linear recurrences associated to rays in Pascal’s triangle and combinatorial identities 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © 2014 Mathematical Institute, Slovak Academy of Sciences Abstract Our main purpose is to describe the recurrence relation associated to the sum of diagonal elements laying along a finite ray crossing Pascal’s triangle. We precise the generating function of the sequence of described sums. We also answer a question of Horadam posed in his paper [Chebyshev and Pell connections, Fibonacci Quart. 43 (2005), 108–121]. Further, using Morgan-Voyce sequence, we establish the nice identity $F_{n + 1} - iF_n = i^n \sum\limits_{k = 0}^n {(_{2k}^{n + k} )( - 2 - i)^k } $ of Fibonacci numbers, where i is the imaginary unit. Finally, connections to continued fractions, bivariate polynomials and finite differences are given. Pascal triangles linear recurrences combinatorial properties Komatsu, Takao aut Szalay, László aut Enthalten in Mathematica Slovaca Versita, 1976 64(2014), 2 vom: 01. Apr., Seite 287-300 (DE-627)129564028 (DE-600)223018-5 (DE-576)015031500 0139-9918 nnns volume:64 year:2014 number:2 day:01 month:04 pages:287-300 https://doi.org/10.2478/s12175-014-0203-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_2088 AR 64 2014 2 01 04 287-300 |
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Abstract Our main purpose is to describe the recurrence relation associated to the sum of diagonal elements laying along a finite ray crossing Pascal’s triangle. We precise the generating function of the sequence of described sums. We also answer a question of Horadam posed in his paper [Chebyshev and Pell connections, Fibonacci Quart. 43 (2005), 108–121]. Further, using Morgan-Voyce sequence, we establish the nice identity $F_{n + 1} - iF_n = i^n \sum\limits_{k = 0}^n {(_{2k}^{n + k} )( - 2 - i)^k } $ of Fibonacci numbers, where i is the imaginary unit. Finally, connections to continued fractions, bivariate polynomials and finite differences are given. © 2014 Mathematical Institute, Slovak Academy of Sciences |
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Abstract Our main purpose is to describe the recurrence relation associated to the sum of diagonal elements laying along a finite ray crossing Pascal’s triangle. We precise the generating function of the sequence of described sums. We also answer a question of Horadam posed in his paper [Chebyshev and Pell connections, Fibonacci Quart. 43 (2005), 108–121]. Further, using Morgan-Voyce sequence, we establish the nice identity $F_{n + 1} - iF_n = i^n \sum\limits_{k = 0}^n {(_{2k}^{n + k} )( - 2 - i)^k } $ of Fibonacci numbers, where i is the imaginary unit. Finally, connections to continued fractions, bivariate polynomials and finite differences are given. © 2014 Mathematical Institute, Slovak Academy of Sciences |
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Abstract Our main purpose is to describe the recurrence relation associated to the sum of diagonal elements laying along a finite ray crossing Pascal’s triangle. We precise the generating function of the sequence of described sums. We also answer a question of Horadam posed in his paper [Chebyshev and Pell connections, Fibonacci Quart. 43 (2005), 108–121]. Further, using Morgan-Voyce sequence, we establish the nice identity $F_{n + 1} - iF_n = i^n \sum\limits_{k = 0}^n {(_{2k}^{n + k} )( - 2 - i)^k } $ of Fibonacci numbers, where i is the imaginary unit. Finally, connections to continued fractions, bivariate polynomials and finite differences are given. © 2014 Mathematical Institute, Slovak Academy of Sciences |
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2024-07-04T05:54:31.369Z |
| _version_ |
1803626711728783360 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC213639827X</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230810072906.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230810s2014 xx ||||| 00| ||und c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.2478/s12175-014-0203-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC213639827X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-B1597)s12175-014-0203-0-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Belbachir, Hacène</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Linear recurrences associated to rays in Pascal’s triangle and combinatorial identities</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2014</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© 2014 Mathematical Institute, Slovak Academy of Sciences</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Our main purpose is to describe the recurrence relation associated to the sum of diagonal elements laying along a finite ray crossing Pascal’s triangle. We precise the generating function of the sequence of described sums. We also answer a question of Horadam posed in his paper [Chebyshev and Pell connections, Fibonacci Quart. 43 (2005), 108–121]. Further, using Morgan-Voyce sequence, we establish the nice identity $F_{n + 1} - iF_n = i^n \sum\limits_{k = 0}^n {(_{2k}^{n + k} )( - 2 - i)^k } $ of Fibonacci numbers, where i is the imaginary unit. Finally, connections to continued fractions, bivariate polynomials and finite differences are given.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Pascal triangles</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">linear recurrences</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">combinatorial properties</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Komatsu, Takao</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Szalay, László</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Mathematica Slovaca</subfield><subfield code="d">Versita, 1976</subfield><subfield code="g">64(2014), 2 vom: 01. Apr., Seite 287-300</subfield><subfield code="w">(DE-627)129564028</subfield><subfield code="w">(DE-600)223018-5</subfield><subfield code="w">(DE-576)015031500</subfield><subfield code="x">0139-9918</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:64</subfield><subfield code="g">year:2014</subfield><subfield code="g">number:2</subfield><subfield code="g">day:01</subfield><subfield code="g">month:04</subfield><subfield code="g">pages:287-300</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.2478/s12175-014-0203-0</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_267</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2018</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">64</subfield><subfield code="j">2014</subfield><subfield code="e">2</subfield><subfield code="b">01</subfield><subfield code="c">04</subfield><subfield code="h">287-300</subfield></datafield></record></collection>
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