A147621 -id:A147621 - cp's OEIS frontend

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

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

Roger L. Bagula, Nov 08 2008

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-1,-2,0,5,0,-2,-1,-1,2,1,-1).

Cf. A147607, A147620, A147621.

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

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 *)

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

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

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

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

A147620 Expansion of g.f.: 1/((1 - x - x^2 + x^6 - x^8)*(1 - x^2 + x^6 + x^7 - x^8)).

Original entry on oeis.org

1, 1, 3, 4, 8, 12, 19, 29, 46, 70, 111, 170, 271, 422, 668, 1048, 1655, 2603, 4104, 6453, 10167, 15989, 25175, 39599, 62329, 98064, 154335, 242845, 382183, 601399, 946451, 1489366, 2343847, 3688412, 5804459, 9134287, 14374533, 22620800, 35597998

Offset: 0

Roger L. Bagula, Nov 08 2008

nonn

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-1,0,-2,0,5,0,-2,0,-1,-1,2,1,-1).

Cf. A147607, A147617, A147621.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1-x-x^2+x^6- x^8)*(1-x^2+x^6+x^7-x^8)) )); // G. C. Greubel, Oct 24 2022

f[x_]= -1+x^2-x^6-x^7+x^8;
CoefficientList[Series[-1/(x^8*f[x]*f[1/x]), {x, 0, 50}], x]

Vec(1/(1-x-2*x^2+x^3+x^4+2*x^6-5*x^8+2*x^10+x^12+x^13-2*x^14-x^15+x^16) + O(x^40)) \\ Jinyuan Wang, Mar 10 2020

def A147620_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x-x^2+x^6-x^8)*(1-x^2+x^6+x^7-x^8)) ).list()
A147620_list(40) # G. C. Greubel, Oct 24 2022

G.f.: 1/(1 - x - 2*x^2 + x^3 + x^4 + 2*x^6 - 5*x^8 + 2*x^10 + x^12 + x^13 - 2*x^14 - x^15 + x^16).

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

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

SageMath

Formula

Extensions