A121653 - OEIS

%I #3 Mar 30 2012 18:36:58

%S 1,1,1,1,2,3,4,6,9,13,19,28,41,67,102,150,243,378,568,895,1390,2115,

%T 3366,5229,7974,12687,19785,30307,47893,74761,115063,181457,283143,

%U 436831,687963,1073820,1659809,2608418,4072442,6306619,9980210,15617469

%N G.f.: A(x) = 1/(1 - x*B(x^3)), where B(x) = Sum_{n>=0} a(n)^3*x^n is the g.f. of A121652.

%F a(n) = A121652(n)^(1/3).

%e A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 6*x^7 + 9*x^8 +...

%e The coefficients of 1 - 1/A(x) equal the cube of each term:

%e 1/A(x) = 1 - x - x^4 - x^7 - x^10 - 8*x^13 - 27*x^16 - 64*x^19 - 216*x^22 -... - a(n)^3*x^(3*n+1) -...

%o (PARI) {a(n)=local(B);if(n==0,1,B=sum(k=0,n\3,a(k)^3*x^(3*k)); polcoeff(1/(1-x*B+x*O(x^n)),n))}

%Y Cf. A121652; trisections: A121654, A121655, A121656.

%K nonn

%O 0,5

%A _Paul D. Hanna_, Aug 14 2006