A233896 G.f. satisfies: A(x) = 1 + x*A(x)^2*A(-x)^2 + x^2*(A(x)^2 + A(-x)^2).

1, 1, 2, 6, 10, 33, 72, 236, 572, 1964, 4800, 16910, 42354, 150670, 386992, 1390176, 3622696, 13128940, 34580568, 126131776, 335409928, 1229708169, 3295834080, 12137093684, 32738710652, 121016095812, 328220839472, 1217132137132, 3316783066620, 12333770952588

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Example

G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 10*x^4 + 33*x^5 + 72*x^6 + 236*x^7 +...
Related series:
A(x)^2 = 1 + 2*x + 5*x^2 + 16*x^3 + 36*x^4 + 110*x^5 + 286*x^6 + 868*x^7 +...
A(x)*A(-x) = 1 + 3*x^2 + 12*x^4 + 82*x^6 + 664*x^8 + 5479*x^10 + 47568*x^12 +...
A(x)^2*A(-x)^2 = 1 + 6*x^2 + 33*x^4 + 236*x^6 + 1964*x^8 + 16910*x^10 +...
A(x)^2+A(-x)^2 = 2 + 10*x^2 + 72*x^4 + 572*x^6 + 4800*x^8 + 42354*x^10 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*A^2*subst(A^2, x, -x)+x^2*(A^2+subst(A^2, x, -x+x*O(x^n))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A208887, A143926, A233895.

Sequence in context: A283846 A321727 A145541 * A118039 A218965 A248821

Adjacent sequences: A233893 A233894 A233895 * A233897 A233898 A233899

Keyword

nonn

Author

Paul D. Hanna, Dec 17 2013

Status

approved