A093126 -id:A093126

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A113299

Expansion of solution to an algebraic functional equation.

+10
0

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

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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.

KEYWORD

nonn

AUTHOR

Michael Somos, Oct 24 2005

STATUS

approved

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