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%I M2590 #41 Jun 17 2022 14:45:20
%S 1,3,6,15,46,148,522,1869,6910,25767,97256,369127,1409362,5401698,
%T 20778162,80149210,309945150,1201140154,4663660518,18137774091,
%U 70646533096,275537046276,1075960410806,4206210234205,16459717112530,64469413339498,252727724406852
%N Number of board configurations in Mu Torere (for one player).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A005655/b005655.txt">Table of n, a(n) for n = 0..200</a>
%H Marcia Ascher, <a href="http://www.jstor.org/stable/2690304">Mu torere: an analysis of a Maori game</a>, Math. Mag. 60 (1987), no. 2, 90-100.
%H R. K. Guy & N. J. A. Sloane, <a href="/A005648/a005648.pdf">Correspondence, 1985</a>
%F a(n) = 2*A005654(n) + A005648(n).
%t 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 *)
%o (PARI) C(n,k)=if(k<0||k>n,0,n!/k!/(n-k)!);
%o 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)) )
%Y Cf. A000984, A005654, A005648.
%K nonn,easy,nice
%O 0,2
%A _N. J. A. Sloane_
%E Better description and more terms from _Michael Somos_