A008759 Expansion of (1+x^16)/(1-x)/(1-x^2)/(1-x^3).

1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 24, 27, 31, 34, 39, 43, 48, 53, 59, 64, 71, 77, 84, 91, 99, 106, 115, 123, 132, 141, 151, 160, 171, 181, 192, 203, 215, 226, 239, 251, 264, 277, 291, 304, 319

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,-1,-1,1).

Maple

seq(coeff(series((1+x^16)/((1-x)*(1-x^2)*(1-x^3)), x, n+1), x, n), n = 1 .. 60); # G. C. Greubel, Aug 09 2019

Mathematica

CoefficientList[Series[(1+x^16)/(1-x)/(1-x^2)/(1-x^3), {x, 0, 60}], x] (* Harvey P. Dale, Sep 19 2016 *)
Join[{1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14}, LinearRecurrence[{1, 1, 0, -1, -1, 1}, {16, 19, 21, 24, 27, 31}, 48]] (* G. C. Greubel, Aug 09 2019 *)

Prog

(PARI) my(x='x+O('x^60)); Vec((1+x^16)/((1-x)*(1-x^2)*(1-x^3))) \\ G. C. Greubel, Aug 09 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^16)/((1-x)*(1-x^2)*(1-x^3)) )); // G. C. Greubel, Aug 09 2019
(Sage)
def A008759_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x^16)/((1-x)*(1-x^2)*(1-x^3)) ).list()
A008759_list(60) # G. C. Greubel, Aug 09 2019
(GAP) a:=[16, 19, 21, 24, 27, 31];; for n in [7..60] do a[n]:=a[n-1]+a[n-2]-a[n-4] -a[n-5]+a[n-6]; od; Concatenation([1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14], a); # G. C. Greubel, Aug 09 2019

Crossrefs

Sequence in context: A069905 A008761 A008760 * A008758 A370747 A008757

Adjacent sequences: A008756 A008757 A008758 * A008760 A008761 A008762

Keyword

nonn

Author

N. J. A. Sloane

Status

approved