OFFSET
1,1
COMMENTS
Also the number of vertex covers and independent vertex sets of the n X n bishop graph.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..320
Vaclav Kotesovec, Non-attacking chess pieces
Eric Weisstein's World of Mathematics, Bishop Graph
Eric Weisstein's World of Mathematics, Independent Vertex Set
Eric Weisstein's World of Mathematics, Vertex Cover
FORMULA
MATHEMATICA
knbishops[k_, n_]:=(If[n==1, If[k==1, 1, 0], (-1)^k/(2n-k)!
*Sum[Binomial[2n-k, n-k+i]*Sum[(-1)^m*Binomial[n-i, m]*m^Floor[n/2]*(m+1)^Floor[(n+1)/2], {m, 1, n-i}]
*Sum[(-1)^m*Binomial[n-k+i, m]*m^Floor[(n+1)/2]*(m+1)^Floor[n/2], {m, 1, n+i-k}], {i, Max[0, k-n], Min[k, n]}]]);
Table[1+Sum[knbishops[k, n], {k, 1, 2n-1}], {n, 1, 25}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Dec 06 2011
STATUS
approved