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%I #23 Aug 18 2024 11:16:38
%S 1,0,1,1,2,1,3,2,4,4,5,5,8,7,9,10,12,12,16,15,19,20,23,23,29,28,33,35,
%T 39,40,47,47,53,56,61,63,72,72,80,84,91,93,104,105,115,120,128,132,
%U 145,147,158,165,175,180,195,198,212,220,232,238,256,260,276,286,300,308
%N Expansion of 1/((1-x^2)(1-x^3)(1-x^4)(1-x^9)).
%C Number of partitions of n into parts 2, 3, 4, and 9. - _Joerg Arndt_, Aug 14 2013
%H Vincenzo Librandi, <a href="/A029139/b029139.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1,-1,-1,-1,0,2,0,-1,-1,-1,1,1,1,0,-1).
%F a(n) = floor((2*n^3 + 54*n^2 + 431*n + 2247 + 81*(n+9)*(-1)^n + 192*cos(2*Pi*n/3)*(floor(n/3)+1))/2592). - _Tani Akinari_, Aug 13 2013
%t CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^4)(1-x^9)), {x, 0, 100}], x] (* _Jinyuan Wang_, Mar 18 2020 *)
%t LinearRecurrence[{0,1,1,1,-1,-1,-1,0,2,0,-1,-1,-1,1,1,1,0,-1},{1,0,1,1,2,1,3,2,4,4,5,5,8,7,9,10,12,12},70] (* _Harvey P. Dale_, Aug 18 2024 *)
%o (PARI) Vec( 1/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^9)) + O(x^66) ) \\ _Joerg Arndt_, Aug 14 2013
%o (PARI) a(n)=round((2*n^3+54*n^2+399*n+899)/2592+(n%3==0)*n/27+(n+9)*(-1)^n/32) \\ _Tani Akinari_, Jun 03 2014
%K nonn,easy
%O 0,5
%A _N. J. A. Sloane_