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%I #22 Sep 08 2022 08:44:50
%S 1,0,1,1,1,2,2,2,3,3,4,4,6,5,7,8,8,10,11,11,14,14,16,17,20,20,23,25,
%T 26,29,32,32,37,38,41,44,48,49,54,57,60,64,69,70,77,80,84,89,95,97,
%U 105,109,114,120,127,130,139,144,150,157,166,169,180,186
%N Expansion of 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^12)).
%C a(n) is the number of partitions of n into parts 2, 3, 5, and 12. [_Joerg Arndt_, Jan 10 2018]
%H Vincenzo Librandi, <a href="/A029149/b029149.txt">Table of n, a(n) for n = 0..5000</a>
%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,0,0,-1,-1,0,1,0,1,0,-1,-1,0,0,0,1,1,0,-1).
%F G.f.: 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^12)).
%F a(n) = a(n-2)+a(n-3)-a(n-7)-a(n-8)+a(n-10)+a(n-12)-a(n-14)-a(n-15)+a(n-19)+a(n-20)-a(n-22). - _Wesley Ivan Hurt_, May 20 2021
%t CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^5)(1-x^12)),{x,0,60}],x] (* or *) LinearRecurrence[{0,1,1,0,0,0,-1,-1,0,1,0,1,0,-1,-1,0,0,0,1,1,0,-1},{1,0,1,1,1,2,2,2,3,3,4,4,6,5,7,8,8,10,11,11,14,14},60] (* _Harvey P. Dale_, Jan 08 2018 *)
%o (Magma) m:=100; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^12)))); // _Vincenzo Librandi_, Jan 10 2018
%o (PARI) Vec(1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^12)) + O(x^70)) \\ _Jinyuan Wang_, Feb 28 2020
%K nonn
%O 0,6
%A _N. J. A. Sloane_