cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A113299 Expansion of solution to an algebraic functional equation.

Original entry on oeis.org

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

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Author

Michael Somos, Oct 24 2005

Keywords

Examples

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

Crossrefs

Cf. A001190, A093126.

Programs

  • PARI
    {a(n) = local(A, m); if( n<1, 0, A = 1 + O(x); m=1; while( m

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).
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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