A008772 Expansion of (1+x^11)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

1, 1, 2, 3, 5, 6, 9, 11, 15, 18, 23, 28, 35, 41, 50, 59, 70, 81, 95, 109, 126, 143, 163, 184, 208, 232, 260, 289, 321, 354, 391, 429, 471, 514, 561, 610, 663, 717, 776, 837, 902, 969, 1041, 1115, 1194, 1275, 1361, 1450, 1544, 1640, 1742, 1847, 1957, 2070, 2189, 2311, 2439, 2570, 2707

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

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

Formula

G.f.: (1+x^11)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

Maple

seq(coeff(series((1+x^11)/((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

CoefficientList[Series[(1+x^11)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4), {x, 0, 60}], x] (* Wesley Ivan Hurt, Apr 08 2017 *)
Join[{1, 1}, LinearRecurrence[{2, -1, 1, -1, -1, 1, -1, 2, -1}, {2, 3, 5, 6, 9, 11, 15, 18, 23}, 60]] (* Vincenzo Librandi, Apr 09 2017 *)

Prog

(PARI) Vec((1+x^11)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4) + O(x^60)) \\ Michel Marcus, Apr 08 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^11)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)) )); // G. C. Greubel, Sep 10 2019
(Sage)
def A008772_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^11)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))).list()
A008772_list(60) # G. C. Greubel, Sep 10 2019
(GAP) a:=[2, 3, 5, 6, 9, 11, 15, 18, 23];; for n in [10..60] do a[n]:=2*a[n-1]-a[n-2]+a[n-3]-a[n-4]-a[n-5]+a[n-6]-a[n-7]+2*a[n-8]-a[n-9]; od; Concatenation([1, 1], a); # G. C. Greubel, Sep 10 2019

Crossrefs

Sequence in context: A372703 A350897 A008773 * A351003 A008771 A309831

Adjacent sequences: A008769 A008770 A008771 * A008773 A008774 A008775

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms added by G. C. Greubel, Sep 10 2019

Status

approved