%I #8 May 14 2017 00:00:20
%S 1,1,2,3,4,5,7,8,10,12,14,16,20,22,26,30,34,38,44,48,54,60,66,72,81,
%T 87,96,105,114,123,135,144,156,168,180,192,208,220,236,252,268,284,
%U 304,320,340,360,380,400,425,445
%N Expansion of 1/((1-x)(1-x^2)(1-x^3)(1-x^12)).
%C Number of partitions of n into parts 1, 2, 3 and 12. - _Ilya Gutkovskiy_, May 13 2017
%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, -1, -1, 1, 0, 0, 0, 0, 0, 1, -1, -1, 0, 1, 1, -1).
%F a(0)=1, a(1)=1, a(2)=2, a(3)=3, a(4)=4, a(5)=5, a(6)=7, a(7)=8, a(8)=10, a(9)=12, a(10)=14, a(11)=16, a(12)=20, a(13)=22, a(14)=26, a(15)=30, a(16)=34, a(17)=38, a(n)=a(n-1)+a(n-2)-a(n-4)-a(n-5)+a(n-6)+ a(n-12)- a(n-13)- a(n-14)+a(n-16)+a(n-17)-a(n-18). - _Harvey P. Dale_, Nov 01 2015
%t CoefficientList[Series[1/((1-x)(1-x^2)(1-x^3)(1-x^12)),{x,0,50}],x] (* or *) LinearRecurrence[{1,1,0,-1,-1,1,0,0,0,0,0,1,-1,-1,0,1,1,-1},{1,1,2,3,4,5,7,8,10,12,14,16,20,22,26,30,34,38},50] (* _Harvey P. Dale_, Nov 01 2015 *)
%K nonn
%O 0,3
%A _N. J. A. Sloane_.