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%I M0376 #16 Jul 23 2022 19:26:06
%S 0,1,0,2,2,8,14,36,112,216,928,1440,8616,11520,87864,100800,997952,
%T 1008000,12427904,10886400,169435936,130636800,2501216992,1676505600,
%U 39837528576,23471078400,679494214656,348713164800,12370158205568,5579410636800,239109033342848
%N Bishops on an n X n board (see Robinson paper for details).
%D R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). [The sequence mu(n).]
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H R. W. Robinson, <a href="/A000899/a000899_1.pdf">Counting arrangements of bishops</a>, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). (Annotated scanned copy)
%p For Maple program see A005635.
%t d[n_] := d[n] = If[n <= 1, 1, d[n - 1] + (n - 1)*d[n - 2]];
%t M[n_] := Module[{k}, If[Mod[n, 2] == 0, k = n/2; If[Mod[k, 2] == 0, Return[k!*(k + 2)/2], Return[(k - 1)!*(k + 1)^2/2]], k = (n - 1)/2; Return[d[k]*d[k + 1]]]];
%t B[n_] := B[n] = Which[n == 0 || n == -2, 1, OddQ[n], B[n - 1], True, 2*B[n - 2] + (n - 2)*B[n - 4]];
%t S[n_] := S[n] = Module[{k}, If[Mod[n, 2]==0, 0, k = (n-1)/2; B[k]*B[k+1]]];
%t a[n_] := (M[n] - S[n])/2;
%t Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Jul 23 2022, after Maple program in A005635 *)
%K nonn
%O 1,4
%A _N. J. A. Sloane_.
%E More terms from _N. J. A. Sloane_, Sep 28 2006
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