A008771 Expansion of (1+x^10)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

1, 1, 2, 3, 5, 6, 9, 11, 15, 18, 24, 28, 36, 42, 52, 60, 73, 83, 99, 112, 131, 147, 170, 189, 216, 239, 270, 297, 333, 364, 405, 441, 487, 528, 580, 626, 684, 736, 800, 858, 929, 993, 1071, 1142, 1227, 1305, 1398, 1483, 1584, 1677, 1786, 1887, 2005, 2114, 2241, 2359, 2495, 2622, 2768

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 (1,2,-1,-2,-1,2,1,-1).

Maple

seq(coeff(series((1+x^10)/((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^10)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4), {x, 0, 60}], x] (* Harvey P. Dale, Oct 28 2013 *)
LinearRecurrence[{1, 2, -1, -2, -1, 2, 1, -1}, {1, 1, 2, 3, 5, 6, 9, 11, 15}, 60]

Prog

(PARI) my(x='x+O('x^60)); Vec((1+x^10)/((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^10)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)) )); // G. C. Greubel, Sep 10 2019
(Sage)
def A008771_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^10)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))).list()
A008771_list(60) # G. C. Greubel, Sep 10 2019
(GAP) a:=[1, 2, 3, 5, 6, 9, 11, 15];; for n in [9..60] do a[n]:=a[n-1]+2*a[n-2] -a[n-3]-2*a[n-4]-a[n-5]+2*a[n-6]+a[n-7]-a[n-8]; od; Concatenation([1], a); # G. C. Greubel, Sep 10 2019

Crossrefs

Sequence in context: A008773 A008772 A351003 * A309831 A309830 A008770

Adjacent sequences: A008768 A008769 A008770 * A008772 A008773 A008774

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Terms a(46) onward added by G. C. Greubel, Sep 10 2019

Status

approved