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%I #11 Jul 30 2015 23:16:24
%S 1,0,0,0,0,0,1,1,1,0,0,0,2,1,2,1,1,0,2,2,3,2,2,1,4,2,4,3,4,2,5,4,6,4,
%T 5,4,8,5,8,6,8,5,10,8,11,8,10,8,14,10,14,11,14,10,17,14,19,14,17,14,
%U 22,17,23,19,23,17,26,22,29
%N Expansion of 1/((1-x^6)(1-x^7)(1-x^8)(1-x^12)).
%H <a href="/index/Rec#order_33">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, -1, -1, -1, 0, 0, -1, -1, -1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, -1).
%F a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=1, a(7)=1, a(8)=1, a(9)=0, a(10)=0, a(11)=0, a(12)=2, a(13)=1, a(14)=2, a(15)=1, a(16)=1, a(17)=0, a(18)=2, a(19)=2, a(20)=3, a(21)=2, a(22)=2, a(23)=1, a(24)=4, a(25)=2, a(26)=4, a(27)=3, a(28)=4, a(29)=2, a(30)=5, a(31)=4, a(32)=6, a(n)=a(n-6)+a(n-7)+a(n-8)+a(n-12)-a(n-13)-a(n-14)-a(n-15)-a(n-18)- a(n-19)- a(n-20)+a(n-21)+a(n-25)+a(n-26)+a(n-27)-a(n-33). - _Harvey P. Dale_, Apr 13 2015
%t CoefficientList[Series[1/((1-x^6)(1-x^7)(1-x^8)(1-x^12)),{x,0,70}],x] (* or *) LinearRecurrence[{0,0,0,0,0,1,1,1,0,0,0,1,-1,-1,-1,0,0,-1,-1,-1,1,0,0,0,1,1,1,0,0,0,0,0,-1},{1,0,0,0,0,0,1,1,1,0,0,0,2,1,2,1,1,0,2,2,3,2,2,1,4,2,4,3,4,2,5,4,6},70] (* _Harvey P. Dale_, Apr 13 2015 *)
%o (PARI) Vec(1/((1-x^6)*(1-x^7)*(1-x^8)*(1-x^12))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012
%K nonn,easy
%O 0,13
%A _N. J. A. Sloane_.
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