A093113 Coefficients of the solution to a functional equation.

1, 2, 6, 16, 62, 192, 652, 2048, 9270, 31744, 116948, 393216, 1533868, 5341184, 19445016, 67108864, 332958758, 1215037440, 4711687300, 16642998272, 67697833092, 245257732096, 923984441000, 3298534883328, 13952454631996

Offset

1,2

Comments

G.f. A(x) satisfies A(4*x^2) = A(x) + A(-x) = -4*A(x)*A(-x). Also A(4*x^2) = 4 * A(x)^2/(1 + 4*A(x)).

Links

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

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=A/2+sqrt(A^2/4+A)); polcoeff(A, n)*4^(n-1))

Crossrefs

Sequence in context: A324062 A033301 A197102 * A150030 A150031 A121753

Adjacent sequences: A093110 A093111 A093112 * A093114 A093115 A093116

Keyword

nonn

Author

Michael Somos, Mar 20 2004

Status

approved