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A005655
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Board configurations in Mu Torere (for one player).
(Formerly M2590)
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| Ascher, Marcia; Mu torere: an analysis of a Maori game. Math. Mag. 60 (1987), no. 2, 90-100.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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}] (* From Jean-François Alcover, Jan 27 2012, after Pari *)
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PROG
| (PARI) 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)) ) where C(n, k)=if(k<0|k>n, 0, n!/k!/(n-k)!)
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CROSSREFS
| Cf. A000984, A005654, A005648. a(n)=2*A005654(n)+A005648(n).
Sequence in context: A067771 A056382 A028401 * A051169 A051610 A102356
Adjacent sequences: A005652 A005653 A005654 * A005656 A005657 A005658
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Better description and more terms from Michael Somos
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