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Expansion of 1/((1-x^8)(1-x^9)(1-x^10)(1-x^11)).
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%I #12 Apr 18 2023 20:10:32

%S 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,

%T 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,

%U 12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,21,21,22,22,23,23,24

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

%C 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

%H <a href="/index/Rec#order_38">Index entries for linear recurrences with constant coefficients</a>, 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).

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

%F 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

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

%o (PARI) Vec(1/((1-x^8)*(1-x^9)*(1-x^10)*(1-x^11)) + O(x^80)) \\ _Jinyuan Wang_, Mar 11 2020

%K nonn

%O 0,19

%A _N. J. A. Sloane_

%E More terms from _Stefan Steinerberger_, Apr 09 2006