A092421 Coefficients of the solution to a functional equation.

1, 3, 6, 9, 12, 18, 27, 27, 15, 36, 108, 54, -207, 81, 1296, 81, -5397, 45, 25245, 108, -118053, 324, 563355, 162, -2711799, -621, 13188096, 243, -64689894, 3888, 319651920, 243, -1589538684, -16191, 7949000070, 135, -39951345438, 75735

Offset

1,2

Links

Table of n, a(n) for n=1..38.

Formula

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

Example

x + 3*x^2 + 6*x^3 + 9*x^4 + 12*x^5 + 18*x^6 + 27*x^7 + 27*x^8 + ...

Prog

(PARI) {a(n) = local(A, m); if( n<1, 0, A = x + O(x^2); m=1; while( m<=n, m*=2; A = subst(A, x, x^2); A = 3*A + sqrt(A + 9*A^2)); polcoeff(A, n))}

Crossrefs

Sequence in context: A173195 A354785 A232920 * A109657 A175589 A348339

Adjacent sequences: A092418 A092419 A092420 * A092422 A092423 A092424

Keyword

sign

Author

Michael Somos, Mar 22 2004

Status

approved