A005655 Number of board configurations in Mu Torere (for one player).
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
References
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Marcia Ascher, Mu torere: an analysis of a Maori game, Math. Mag. 60 (1987), no. 2, 90-100.
- R. K. Guy & N. J. A. Sloane, Correspondence, 1985
Programs
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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 *)
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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)) )
Extensions
Better description and more terms from Michael Somos