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%I #3 Mar 30 2012 18:36:58
%S 1,1,4,13,41,150,568,2115,7974,30307,115063,436831,1659809,6306619,
%T 24210855,93152526,357925365,1384070472,5365825156,20791117843,
%U 80784911668,314369613909,1223297887923,4773716056341,18647712778338
%N A trisection of A121653; a(n) = A121653(3*n) = A121652(3*n)^(1/3).
%F G.f.: A(x) = 1/(1 - x*B(x)^3), where B(x) = Sum_{n>=0} A121653(n)^3*x^n is the g.f. of A121652.
%e G.f.: A(x) = 1 + x + 4*x^2 + 13*x^3 + 41*x^4 + 150*x^5 + 568*x^6 +...
%e 1/A(x) = 1 - x - 3*x^2 - 6*x^3 - 10*x^4 - 36*x^5 - 141*x^6 -...
%e 1/A(x) = 1 - x*B(x)^3, where
%e B(x)^3 = 1 + 3*x + 6*x^2 + 10*x^3 + 36*x^4 + 141*x^5 + 436*x^6 +...
%e and B(x) is g.f. of A121652 where all coefficients are cubes:
%e B(x) = 1 + x + x^2 + x^3 + 8*x^4 + 27*x^5 + 64*x^6 + 216*x^7 +...
%e Notice that coefficients are related by A121652(n) = A121653(n)^3.
%o (PARI) {a(n)=local(B=1+x);if(n==0, 1, for(m=0,n,B=1/(1-x*sum(k=0,m,polcoeff(B,k)^3*x^(3*k))+O(x^(3*n+3)))); polcoeff(B,3*n))}
%Y Cf. A121652, A121653; A121655, A121656.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 14 2006
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