A237650 G.f. satisfies: A(x) = (1+x+x^2)^3 * A(x^2)^2.

1, 3, 12, 25, 75, 144, 357, 615, 1380, 2285, 4767, 7488, 14817, 22707, 43068, 63769, 116667, 169584, 301589, 427815, 741396, 1037149, 1761087, 2418432, 4025153, 5465955, 8956716, 11986009, 19330347, 25633296, 40835973, 53508711, 84129156, 109392269, 170278047, 219206976

Offset

0,2

Links

Table of n, a(n) for n=0..35.

Formula

The odd-indexed bisection of A195586.

The 3rd self-convolution of A237651.

G.f. A(x) satisfies:

(1) A(x) = Product_{n>=0} ( 1 + x^(2^n) + x^(2*2^n) )^(3*2^n).

(2) A(x) / A(-x) = (1+x+x^2)^3 / (1-x+x^2)^3.

Example

G.f.: A(x) = 1 + 3*x + 12*x^2 + 25*x^3 + 75*x^4 + 144*x^5 + 357*x^6 +...
where:
A(x) = (1+x+x^2)^3 * (1+x^2+x^4)^6 * (1+x^4+x^8)^12 * (1+x^8+x^16)^24 * (1+x^16+x^32)^48 *...* (1 + x^(2^n) + x^(2*2^n))^(3*2^n) *...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, #binary(n), A=(1+x+x^2)^3*subst(A^2, x, x^2) +x*O(x^n)); polcoeff(A, n)}
for(n=0, 50, print1(a(n), ", "))
(PARI) {a(n)=local(A=1+x); A=prod(k=0, #binary(n), (1+x^(2^k)+x^(2*2^k)+x*O(x^n))^(3*2^k)); polcoeff(A, n)}
for(n=0, 50, print1(a(n), ", "))

Crossrefs

Cf. A195586, A237651, A237647.

Sequence in context: A068967 A071355 A366984 * A199242 A326725 A169678

Adjacent sequences: A237647 A237648 A237649 * A237651 A237652 A237653

Keyword

nonn

Author

Paul D. Hanna, May 04 2014

Status

approved