A237651 G.f. satisfies: A(x) = (1+x+x^2) * A(x^2)^2.

1, 1, 3, 2, 9, 7, 17, 10, 41, 31, 75, 44, 150, 106, 238, 132, 445, 313, 711, 398, 1251, 853, 1859, 1006, 3135, 2129, 4677, 2548, 7590, 5042, 10734, 5692, 16865, 11173, 23979, 12806, 36911, 24105, 50551, 26446, 75985, 49539, 104683, 55144, 155140, 99996, 207188, 107192, 300766, 193574, 403994

Offset

0,3

Links

Table of n, a(n) for n=0..50.

Formula

The odd-indexed bisection equals the self-convolution of this sequence.

The self-convolution cube yields A237650, the odd-indexed bisection of A195586.

G.f. A(x) satisfies:

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

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

Example

G.f.: A(x) = 1 + x + 3*x^2 + 2*x^3 + 9*x^4 + 7*x^5 + 17*x^6 + 10*x^7 +...
where:
A(x) = (1+x+x^2) * (1+x^2+x^4)^2 * (1+x^4+x^8)^4 * (1+x^8+x^16)^8 * (1+x^16+x^32)^16 *...* (1 + x^(2^n) + x^(2*2^n))^(2^n) *...

Prog

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

Crossrefs

Cf. A002487, A195586, A237650.

Sequence in context: A274925 A084398 A118306 * A124003 A159588 A321572

Adjacent sequences: A237648 A237649 A237650 * A237652 A237653 A237654

Keyword

nonn

Author

Paul D. Hanna, May 04 2014

Status

approved