A213263 G.f. satisfies: A(x) = x + A( A(x)^2/(1 + A(x)) ).

1, 1, 1, 2, 5, 12, 30, 80, 219, 609, 1724, 4953, 14388, 42193, 124768, 371602, 1113667, 3356017, 10162979, 30911457, 94390590, 289258448, 889304859, 2742205395, 8478653638, 26280715255, 81648362339, 254204771596, 793011895972, 2478427376313, 7759251412310

Offset

1,4

Comments

Compare g.f. to: G(x) = x + G( G(x)^2/(1 + G(x) + G(x)^2) ) when G(x) = x/(1-x).

Links

Table of n, a(n) for n=1..31.

Example

G.f.: A(x) = x + x^2 + x^3 + 2*x^4 + 5*x^5 + 12*x^6 + 30*x^7 + 80*x^8 +...
Related expansions:
A(x)^2 = x^2 + 2*x^3 + 3*x^4 + 6*x^5 + 15*x^6 + 38*x^7 + 98*x^8 +...
A(x)^2/(1 + A(x)) = x^2 + x^3 + x^4 + 3*x^5 + 8*x^6 + 19*x^7 + 49*x^8 +...

Prog

(PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=x+subst(A, x, A^2/(1+A+x*O(x^n)))); polcoeff(A, n)}
for(n=1, 40, print1(a(n), ", "))

Crossrefs

Cf. A213264.

Sequence in context: A101785 A363306 A003089 * A179544 A182488 A363912

Adjacent sequences: A213260 A213261 A213262 * A213264 A213265 A213266

Keyword

nonn

Author

Paul D. Hanna, Jun 07 2012

Status

approved