A113299 Expansion of solution to an algebraic functional equation.

1, 3, 10, 33, 110, 366, 1219, 4059, 13518, 45018, 149924, 499290, 1662787, 5537577, 18441799, 61416729, 204536183, 681166986, 2268490929, 7554756990, 25159612832, 83789077212, 279042826065, 929296530558, 3094836925438

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Formula

G.f. A(x) = x/((1-B(x))^2-x) where B(x) = g.f. for A001190.

G.f. A(x) = B(x) / (1 - 2*B(x)) where B(x) = g.f. for A093126.

G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = v*(1 + 6*u) - u^2*(1 - 8*v).

a(2*n) == 0 (mod 3).

Example

x + 3*x^2 + 10*x^3 + 33*x^4 + 110*x^5 + 366*x^6 + 1219*x^7 + 4059*x^8 +  ...

Prog

(PARI) {a(n) = local(A, m); if( n<1, 0, A = 1 + O(x); m=1; while( m<n, m*=2; A = x * subst(A, x, x^2); A = sqrt( A /(1 - 2*A) / x)); A *= x*A; A /= (1 - A); polcoeff(A, n))}

Crossrefs

Cf. A001190, A093126.

Sequence in context: A006190 A020704 A289450 * A126931 A257178 A257363

Adjacent sequences: A113296 A113297 A113298 * A113300 A113301 A113302

Keyword

nonn

Author

Michael Somos, Oct 24 2005

Status

approved