A143559 G.f. satisfies: A(x) = 1 + x*A(x)^6/A(-x)^6.

1, 1, 12, 72, 1012, 9552, 148764, 1609496, 26398020, 305821344, 5174354988, 62479377384, 1079265357204, 13399747245040, 234917433809724, 2975608178304696, 52748683164797668, 678307369324850496

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

G.f. satisfies: A(x) = 1 + x^2/(1 - A(-x)).

G.f. satisfies: A(x) = 1 + x^2 + x*A(x)^6/A(-x)^5.

G.f. satisfies: (A(x) - 1)^5 = ( 1 - (1+x^2)/A(x) )^6/x = x^5*A(x)^30/A(-x)^30.

G.f.: A(x) = (1+x^2)*G(x) where G(x) = 1 + x*G(x)^6/G(-x)^5.

Example

G.f. A(x) = 1 + x + 12*x^2 + 72*x^3 + 1012*x^4 + 9552*x^5 + 148764*x^6 +...
A(x)/A(-x) = 1 + 2*x + 2*x^2 + 122*x^3 + 242*x^4 + 16002*x^5 + 38962*x^6 +...
A(x)^5/A(-x)^5 = 1 + 10*x + 50*x^2 + 770*x^3 + 6450*x^4 + 109802*x^5 +...
where 1 - (1+x^2)/A(x) = x*A(x)^5/A(-x)^5.

Prog

(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, A=1+x*A^6/subst(A^6, x, -x)); polcoeff(A, n)}

Crossrefs

Cf. A143555, A143556, A143557, A143558.

Sequence in context: A320660 A367700 A108734 * A341542 A120793 A120783

Adjacent sequences: A143556 A143557 A143558 * A143560 A143561 A143562

Keyword

nonn

Author

Paul D. Hanna, Aug 24 2008

Status

approved