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%I #8 Apr 21 2024 22:59:32
%S 1,0,0,0,1,0,0,1,1,0,0,2,2,0,1,2,2,0,2,3,2,1,3,4,3,2,4,4,4,3,5,5,5,5,
%T 6,7,7,6,7,8,9,7,9,10,11,9,11,13,13,11,13,15,15,13,16,18,18,16,19,21,
%U 21,19,22,24,24,22,26,28,28
%N Expansion of 1/((1-x^4)(1-x^7)(1-x^11)(1-x^12)).
%H <a href="/index/Rec#order_34">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, -1, -1, 0, -1, -1, 0, 0, 1,0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1).
%F G.f.: 1/((1-x^4)(1-x^7)(1-x^11)(1-x^12)).
%F a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=1, a(5)=0, a(6)=0, a(7)=1, a(8)=1, a(9)=0, a(10)=0, a(11)=2, a(12)=2, a(13)=0, a(14)=1, a(15)=2, a(16)=2, a(17)=0, a(18)=2, a(19)=3, a(20)=2, a(21)=1, a(22)=3, a(23)=4, a(24)=3, a(25)=2, a(26)=4, a(27)=4, a(28)=4, a(29)=3, a(30)=5, a(31)=5, a(32)=5, a(33)=5, a(n)= a(n-4)+a(n-7)+a(n-12)-a(n-15)-a(n-16)-a(n-18)-a(n-19)+a(n-22)+ a(n-27)+ a(n-30)- a(n-34). - _Harvey P. Dale_, Jun 03 2015
%t CoefficientList[Series[1/((1-x^4)(1-x^7)(1-x^11)(1-x^12)),{x,0,100}],x] (* or *) LinearRecurrence[{0,0,0,1,0,0,1,0,0,0,0,1,0,0,-1,-1,0,-1,-1,0,0,1,0,0,0,0,1,0,0,1,0,0,0,-1},{1,0,0,0,1,0,0,1,1,0,0,2,2,0,1,2,2,0,2,3,2,1,3,4,3,2,4,4,4,3,5,5,5,5},100] (* _Harvey P. Dale_, Jun 03 2015 *)
%K nonn
%O 0,12
%A _N. J. A. Sloane_.