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A005655 Board configurations in Mu Torere (for one player).
(Formerly M2590)
1
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; text; internal format)
OFFSET

0,2

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

FORMULA

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

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-Fran├žois Alcover, Jan 27 2012, after PARI *)

PROG

(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)) )

CROSSREFS

Cf. A000984, A005654, A005648.

Sequence in context: A337326 A056382 A028401 * A277063 A051169 A051610

Adjacent sequences:  A005652 A005653 A005654 * A005656 A005657 A005658

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

Better description and more terms from Michael Somos

STATUS

approved

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Last modified June 19 11:24 EDT 2021. Contains 345127 sequences. (Running on oeis4.)