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.

A005655 Number of board configurations in Mu Torere (for one player).

Original entry on oeis.org

1, 3, 6, 15, 46, 148, 522, 1869, 6910, 25767, 97256, 369127, 1409362, 5401698, 20778162, 80149210, 309945150, 1201140154, 4663660518, 18137774091, 70646533096, 275537046276, 1075960410806, 4206210234205, 16459717112530, 64469413339498, 252727724406852
Offset: 0

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Author

Keywords

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Programs

  • Mathematica
    a[0] = 1; a[n_] := (1/2)*(Binomial[ 2*Quotient[n, 2], Quotient[n, 2]] + 2*(Binomial[ 2n-1, n] + Binomial[ n-1, Quotient[n, 2]]) + Sum[ EulerPhi[n/k] * Binomial[2k, k]/(2n), {k, Divisors[n]}]); Table[ a[n], {n, 0, 24}] (* Jean-François Alcover, Jan 27 2012, after PARI *)
  • PARI
    C(n,k)=if(k<0||k>n,0,n!/k!/(n-k)!);
    a(n)= (1/2) *( C(2*(n\2), n\2) + 2*(C(2*n-1,n)+C(n-1,n\2)) + if(n<1,n >= 0,sumdiv(n,k,eulerphi(n/k)*C(2*k,k))/(2*n)) )

Formula

a(n) = 2*A005654(n) + A005648(n).

Extensions

Better description and more terms from Michael Somos