cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A147617 Expansion of g.f.: 1/((1 - x - x^2 + x^5 - x^7)*(1 - x^2 + x^5 + x^6 - x^7)).

Original entry on oeis.org

1, 1, 3, 4, 8, 10, 17, 24, 37, 55, 85, 132, 202, 317, 488, 761, 1171, 1818, 2802, 4333, 6688, 10334, 15964, 24661, 38115, 58886, 91011, 140619, 217317, 335783, 518882, 801765, 1238908, 1914362, 2958086, 4570887, 7062966, 10913848, 16864199
Offset: 0

Views

Author

Roger L. Bagula, Nov 08 2008

Keywords

Links

Crossrefs

Cf. A147607, A147620, A147621.

Programs

  • Magma
    R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1-x-x^2+x^5- x^7)*(1-x^2+x^5+x^6-x^7)) )); // G. C. Greubel, Oct 24 2022
  • Mathematica
    f[x_]= -1+x+x^2-x^5+x^7;
CoefficientList[Series[-1/(x^7*f[x]*f[1/x]), {x, 0, 50}], x] (* G. C. Greubel, Oct 24 2022 *)
  • PARI
    Vec(1/(1 -x -2*x^2 +x^3 +x^4 +2*x^5 -5*x^7 +2*x^9 +x^10 +x^11 -2*x^12 - x^13 +x^14) + O(x^40)) \\ Jinyuan Wang, Mar 10 2020
  • SageMath
    def A147617_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x-x^2+x^5-x^7)*(1-x^2+x^5+x^6-x^7)) ).list()
A147617_list(40) # G. C. Greubel, Oct 24 2022

Formula

G.f.: 1/(1 - x - 2*x^2 + x^3 + x^4 + 2*x^5 - 5*x^7 + 2*x^9 + x^10 + x^11 - 2*x^12 - x^13 + x^14).
G.f.: -1/(x^7*f(x)*f(1/x)), where f(x) = -1 + x + x^2 - x^5 + x^7. - G. C. Greubel, Oct 24 2022

Extensions

Definition corrected by N. J. A. Sloane, Nov 09 2008

A147598 Expansion of g.f. 1/((1-x^2+x^3+x^4-x^5)*(1-x-x^2+x^3-x^5)).

Original entry on oeis.org

1, 1, 3, 2, 4, 3, 6, 9, 14, 23, 29, 45, 57, 88, 123, 184, 267, 382, 556, 787, 1149, 1643, 2392, 3444, 4978, 7184, 10348, 14956, 21550, 31152, 44924, 64881, 93611, 135101, 195000, 281382, 406201, 586164, 846121, 1221064, 1762399, 2543555, 3671003
Offset: 0

Views

Author

Roger L. Bagula, Nov 08 2008

Keywords

Links

Crossrefs

Cf. A147605, A147606, A147607, A147617, A147620.

Programs

  • Magma
    R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/((1-x^2+x^3+x^4-x^5)*(1-x-x^2+x^3-x^5)) )); // G. C. Greubel, Oct 25 2022
  • Mathematica
    f[x_]= x^5 -x^4 -x^3 +x^2 -1;
CoefficientList[Series[-1/(x^5*f[x]*f[1/x]), {x,0,50}],x]
  • SageMath
    def A147598_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x^2+x^3+x^4-x^5)*(1-x-x^2+x^3-x^5)) ).list()
A147598_list(50) # G. C. Greubel, Oct 25 2022

Formula

G.f.: -1/(x^5*f(x)*f(1/x)), where f(x) = -1 +x^2 -x^3 -x^4 +x^5.
G.f.: 1/((x^5-x^4-x^3+x^2-1)*(x^5-x^3+x^2+x-1)). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009

Extensions

Better name (using g.f.) from Joerg Arndt, Apr 06 2018

A147593 Expansion of 1/(1 - x + x^3 - 3*x^4 + x^5 - x^7 + x^8).

Original entry on oeis.org

1, 1, 1, 0, 2, 3, 5, 3, 6, 8, 16, 16, 24, 28, 50, 61, 91, 109, 170, 220, 327, 415, 607, 800, 1164, 1536, 2192, 2928, 4172, 5616, 7921, 10705, 15049, 20460, 28638, 39027, 54453, 74451, 103662, 141996, 197288, 270704, 375632, 516096, 715258, 983661, 1362091
Offset: 0

Views

Author

Roger L. Bagula, Nov 08 2008

Keywords

Links

Crossrefs

Cf. A147598, A147605, A147606, A147607, A147617, A147620.

Programs

  • Magma
    R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/((1+x^3-x^4)*(1-x-x^4)) )); // G. C. Greubel, Oct 25 2022
  • Mathematica
    f[x_]= x^4-x^3-1; CoefficientList[Series[-1/(x^4*f[x]*f[1/x]), {x,0,50}], x]
  • SageMath
    def A147593_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/((1+x^3-x^4)*(1-x-x^4)) ).list()
A147593_list(50) # G. C. Greubel, Oct 25 2022

Formula

G.f.: -1/(x^4*f(x)*f(1/x)), where f(x) = -1 - x^3 + x^4.
G.f.: 1/((1+x^3-x^4)*(1-x-x^4)). - Colin Barker, Nov 04 2012

Extensions

Edited by Joerg Arndt and Colin Barker, Nov 04 2012.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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