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A029177 Expansion of 1/((1-x^2)(1-x^4)(1-x^5)(1-x^12)).

%I A029177 #21 Mar 15 2020 22:21:23
%S A029177 1,0,1,0,2,1,2,1,3,2,4,2,6,3,7,4,9,6,10,7,13,9,15,10,19,13,21,15,25,
%T A029177 19,28,21,33,25,37,28,43,33,47,37,54,43,59,47,67,54,73,59,82,67,89,73,
%U A029177 99,82,107,89,118,99,127,107,140,118,150,127,164,140,175,150,190,164,203
%N A029177 Expansion of 1/((1-x^2)(1-x^4)(1-x^5)(1-x^12)).
%H A029177 Harvey P. Dale, <a href="/A029177/b029177.txt">Table of n, a(n) for n = 0..1000</a>
%H A029177 <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%H A029177 <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,1,1,-1,-1,0,-1,0,1,1,0,-1,0,-1,-1,1,1,0,1,0,-1).
%F A029177 G.f.: 1/((1-x^2)(1-x^4)(1-x^5)(1-x^12)).
%F A029177 a(n) = -a(-23 - n).
%F A029177 a(n) = A029011(A084964(n) - 2).
%p A029177 M := Matrix(23, (i,j)-> if (i=j-1) or (j=1 and member(i, [2, 4, 5, 11, 12, 18, 19, 21])) then 1 elif j=1 and member(i, [6, 7, 9, 14, 16, 17, 23]) then -1 else 0 fi); a := n -> (M^(n))[1,1]; seq (a(n), n=0..70); # _Alois P. Heinz_, Jul 25 2008
%t A029177 CoefficientList[Series[1/((1-x^2)(1-x^4)(1-x^5)(1-x^12)),{x,0,70}],x] (* _Harvey P. Dale_, May 31 2012 *)
%o A029177 (PARI) a(n)=if(n<-22,-a(-23-n),polcoeff(1/((1-x^2)*(1-x^4)*(1-x^5)*(1-x^12))+x*O(x^n),n))
%Y A029177 Cf. A029011(n) = a(2n) = a(2n+5).
%K A029177 nonn,easy
%O A029177 0,5
%A A029177 _N. J. A. Sloane_