A005632 Bishops on a 2n+1 X 2n+1 board (see Robinson paper for details). (Formerly M3923)

0, 0, 5, 22, 258, 1628, 18052, 145976, 1837272, 18407664, 265312848, 3184567136, 52020223648, 728304073664, 13317701313600, 213083801827200, 4314950946864000, 77669134543011584, 1725980887361498368, 34519618313219995136, 835374767116711506432, 18378244896208168541184

Offset

1,3

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..22.

R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). [The sequence mu(2k+1).]

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

For Maple program see A005635.

Mathematica

c[n_] := Module[{k}, If[Mod[n, 2]==0, Return[0]]; k = (n-1)/2; If[Mod[k, 2] == 0, Return[k*2^(k-1)*((k/2)!)^2], Return[2^k*(((k+1)/2)!)^2]]];
d[n_] := d[n] = If[n <= 1, 1, d[n - 1] + (n - 1)*d[n - 2]];
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]];
S[n_] := S[n] = Module[{k}, If[Mod[n, 2]==0, 0, k = (n-1)/2; B[k]*B[k+1]]];
Q[n_] := Module[{m}, If[Mod[n, 8] != 1, Return[0]]; m = (n-1)/8; ((2*m)!)^2 /(m!)^2];
a[n_] := (c[2n+1] - S[2n+1] - Q[2n+1])/4;
Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Jul 23 2022, after Maple program in A005635 *)

Crossrefs

Sequence in context: A115657 A066865 A183902 * A183408 A298322 A299215

Adjacent sequences: A005629 A005630 A005631 * A005633 A005634 A005635

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from N. J. A. Sloane, Sep 28 2006

Status

approved