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 A122748 Bishops on an n X n board (see Robinson paper for details). 1
 1, 1, 2, 2, 4, 8, 16, 40, 72, 260, 432, 1976, 2880, 17632, 23040, 177248, 201600, 2001680, 2016000, 24879520, 21772800, 338969216, 261273600, 5002865792, 3353011200, 79676972608, 46942156800, 1358997441920, 697426329600, 24740358817280, 11158821273600, 478218277674496 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). (M_n, p. 208) LINKS Table of n, a(n) for n=0..31. R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). (Annotated scanned copy) MAPLE unprotect(D); D:=proc(n) option remember; if n <= 1 then 1 else D(n-1)+(n-1)*D(n-2); fi; end; # Gives A000085 M:=proc(n) local k; if n mod 2 = 0 then k:=n/2; if k mod 2 = 0 then RETURN( k!*(k+2)/2 ); else RETURN( (k-1)!*(k+1)^2/2 ); fi; else k:=(n-1)/2; RETURN(D(k)*D(k+1)); fi; end; MATHEMATICA d[n_] := d[n] = If[n <= 1, 1, d[n - 1] + (n - 1)*d[n - 2]]; a[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]]]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jul 23 2022, after Maple code *) CROSSREFS Sequence in context: A090129 A001137 A123593 * A108774 A063402 A175195 Adjacent sequences: A122745 A122746 A122747 * A122749 A122750 A122751 KEYWORD nonn AUTHOR N. J. A. Sloane, Sep 25 2006 STATUS approved

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Last modified July 13 02:50 EDT 2024. Contains 374265 sequences. (Running on oeis4.)