A069183 Expansion of 1/((1-x)(1-x^2)^2(1-x^3)(1-x^6)).

1, 1, 3, 4, 7, 9, 15, 18, 27, 33, 45, 54, 72, 84, 108, 126, 156, 180, 220, 250, 300, 340, 400, 450, 525, 585, 675, 750, 855, 945, 1071, 1176, 1323, 1449, 1617, 1764, 1960, 2128, 2352, 2548, 2800, 3024, 3312, 3564, 3888, 4176, 4536, 4860, 5265, 5625, 6075

Offset: 0

Author

Rick L. Shepherd, Apr 10 2002

Keywords

• nonn
• easy

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,-1,3,0,-3,1,2,1,-2,-1,1).

Crossrefs

Cf. A029000.

Programs

Magma

R:=PowerSeriesRing(Integers(), 60); Coefficients(R!( 1/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^6)) )); // G. C. Greubel, May 26 2024

Mathematica

CoefficientList[Series[1/((1-x)(1-x^3)(1-x^6)(1-x^2)^2), {x, 0, 100}], x] (* Jinyuan Wang, Mar 15 2020 *)

PARI

a(n) = polcoeff(1/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^6)+x*O(x^n)), n);

Sage

def A069183_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^6)) ).list()
A069183_list(60) # G. C. Greubel, May 26 2024

Formula

G.f.: 1/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^6)).

a(n) = a(n-1) + 2*a(n-2) - a(n-3) - 2*a(n-4) - a(n-5) + 3*a(n-6) - 3*a(n-8) + a(n-9) + 2*a(n-10) + a(n-11) - 2*a(n-12) - a(n-13) + a(n-14). - Wesley Ivan Hurt, May 24 2024