OFFSET
1,3
LINKS
R. W. Robinson, Counting arrangements of bishops, Lect. Notes Math. 560 (1976), 198-214.
FORMULA
For n=4m or n=4m+1, a(n) = (n! + (2m)!*2^(2*m) + (2m)!/m!)/4.
For n=4m+2 or n=4m+3, a(n) = (n! + (2m+1)!*2^(2*m+1))/4.
a(n) = (P(n)+G(n)+2*R(n))/4, where P,G,R are defined in Robinson (1976). See also Maple code in A000903.
MATHEMATICA
a[n_] := (r=Mod[n, 4]; m=(n-r)/4; q=Quotient[n, 2]; n! + q!*2^q + 2*If[r <= 1, (2m)!/m!, 0])/4; Array[a, 23] (* Jean-François Alcover, Dec 06 2015, adapted from PARI *)
PROG
(PARI) { a(n) = ( n! + (n\2)! * 2^(n\2) + 2*if(n%4<=1, (2*(n\4))!/(n\4)! ) )/4; }
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Max Alekseyev, Oct 31 2015
STATUS
approved