OFFSET
0,5
COMMENTS
Number of solutions to the rook problem on an n X n board having a certain symmetry group (see Robinson for details).
A037224 is an essentially identical sequence.
REFERENCES
R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976).
FORMULA
For asymptotics see the Robinson paper.
a(n) = (1/2 + (-1)^(n/2 - 1/4 + (-1)^n/4)/2) * ((n/2 - 3/4 + (-1)^n/4 + (-1)^(n/2 - 1/4 + (-1)^n/4)/2)! / ((n/4 - 3/8 + (-1)^n/8 + (-1)^(n/2 - 1/4 + (-1)^n/4)/4)!)). - Wesley Ivan Hurt, Mar 30 2015
MAPLE
R:=proc(n) local m; if n mod 4 = 2 or n mod 4 = 3 then RETURN(0); fi; m:=floor(n/4); (2*m)!/m!; end;
For Maple program see A000903.
MATHEMATICA
Table[If[MemberQ[{2, 3}, Mod[n, 4]], 0, ((2Floor[n/4])!/Floor[n/4]!)], {n, 0, 50}] (* Harvey P. Dale, Dec 30 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 23 2006
STATUS
approved