A121655 - OEIS

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

%S 1,2,6,19,67,243,895,3366,12687,47893,181457,687963,2608418,9980210,

%T 38267955,146847036,566931450,2192350203,8483412214,32931060365,

%U 127961086743,497417231082,1939118056782,7565621219100,29525286454134

%N A trisection of A121653; a(n) = A121653(3*n+1) = A121652(3*n+1)^(1/3).

%F G.f.: A(x) = B(x)/(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 + 2*x + 6*x^2 + 19*x^3 + 67*x^4 + 243*x^5 + 895*x^6 +...

%e B(x)/A(x) = 1 - x - 3*x^2 - 6*x^3 - 10*x^4 - 36*x^5 - 141*x^6 -...

%e B(x)/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 +...

%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+1))}

%Y Cf. A121652, A121653; A121654, A121656.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Aug 14 2006