A029442 Expansion of 1/((1-x^8)(1-x^9)(1-x^10)(1-x^11)).

1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 2, 2, 2, 1, 1, 0, 1, 1, 2, 3, 3, 3, 3, 2, 2, 2, 2, 3, 4, 4, 5, 4, 5, 4, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 9, 9, 10, 10, 11, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 21, 21, 22, 22, 23, 23, 24

Offset

0,19

Comments

Gives the number of ways one can write n as the sum of 8, 9, 10 and 11 if the order is irrelevant. - Stefan Steinerberger, Apr 09 2006

Links

Table of n, a(n) for n=0..86.

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

Formula

G.f.: 1/((1-x^8)*(1-x^9)*(1-x^10)*(1-x^11)).

a(n) = a(n-8) + a(n-9) + a(n-10) + a(n-11) - a(n-17) - a(n-18) - 2*a(n-19) - a(n-20) - a(n-21) + a(n-27) + a(n-28) + a(n-29) + a(n-30) - a(n-38). - Wesley Ivan Hurt, Apr 18 2023

Mathematica

CoefficientList[Series[1/((1-x^8)(1-x^9)(1-x^10)(1-x^11)), {x, 0, 100}], x] (* Stefan Steinerberger, Apr 09 2006 *)

Prog

(PARI) Vec(1/((1-x^8)*(1-x^9)*(1-x^10)*(1-x^11)) + O(x^80)) \\ Jinyuan Wang, Mar 11 2020

Crossrefs

Sequence in context: A358479 A288160 A275332 * A125917 A071468 A274886

Adjacent sequences: A029439 A029440 A029441 * A029443 A029444 A029445

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Stefan Steinerberger, Apr 09 2006

Status

approved