A008765 Expansion of (1+x^4)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

1, 1, 2, 3, 6, 7, 11, 14, 20, 24, 32, 38, 49, 57, 70, 81, 98, 111, 131, 148, 172, 192, 220, 244, 277, 305, 342, 375, 418, 455, 503, 546, 600, 648, 708, 762, 829, 889, 962, 1029, 1110, 1183, 1271, 1352, 1448, 1536, 1640, 1736, 1849, 1953, 2074, 2187, 2318, 2439, 2579, 2710, 2860, 3000

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-2,0,0,1,1,-1).

Maple

seq(coeff(series((1+x^4)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)), x, n+1), x, n), n = 0 .. 60); # G. C. Greubel, Sep 10 2019

Mathematica

LinearRecurrence[{1, 1, 0, 0, -2, 0, 0, 1, 1, -1}, {1, 1, 2, 3, 6, 7, 11, 14, 20, 24}, 60] (* G. C. Greubel, Sep 10 2019 *)

Prog

(PARI) my(x='x+O('x^60)); Vec((1+x^4)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))) \\ G. C. Greubel, Sep 10 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^4)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)) )); // G. C. Greubel, Sep 10 2019
(Sage)
def A008765_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^4)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))).list()
A008765_list(60) # G. C. Greubel, Sep 10 2019
(GAP) a:=[1, 1, 2, 3, 6, 7, 11, 14, 20, 24];; for n in [11..60] do a[n]:=a[n-1] +a[n-2]-2*a[n-5]+a[n-8]+a[n-9]-a[n-10]; od; a; # G. C. Greubel, Sep 10 2019

Crossrefs

Sequence in context: A002256 A230584 A294176 * A018468 A117115 A308733

Adjacent sequences: A008762 A008763 A008764 * A008766 A008767 A008768

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Terms a(44) onward added by G. C. Greubel, Sep 10 2019

Status

approved