OFFSET
1,2
COMMENTS
Number of minimum dominating sets in the n X n bishop graph. - Eric W. Weisstein, Jun 04 2017
REFERENCES
A. M. Yaglom and I. M. Yaglom, Challenging Mathematical Problems with Elementary Solutions, vol.1, 1987, p.11 and p.83-88.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Bishop Graph
Eric Weisstein's World of Mathematics, Dominating Set
FORMULA
a(n) = (((2*floor(n/4))!)^2/128)*(n^5 + 3*n^4 + n^3 + 35*n^2 + 38*n + 2 - (n^5 - n^4 - 7*n^3 - n^2 - 10*n - 30)*(-1)^n -4*(n^3 + 2*n^2 + n - 4)*n*cos(Pi*n/2) - 2*(n^5 + n^4 - 11*n^3 - 7*n^2 - 2*n + 2)*sin(Pi*n/2)), for n > 1.
MATHEMATICA
Table[If[n==1, 1, ((2*Floor[n/4])!)^2/128*(n^5+3*n^4+n^3+35*n^2+38*n+2-(n^5-n^4-7*n^3-n^2-10*n-30)*(-1)^n-4*(n^3+2*n^2+n-4)*n*Cos[Pi*n/2]-2*(n^5+n^4-11*n^3-7*n^2-2*n+2)*Sin[Pi*n/2])], {n, 1, 25}]
PROG
(PARI) a(n)={if(n==1, 1, (n\4*2)!^2*if(n%4<2, if(n%2==0, (n+1)^2, (n^3 + 3*n^2 + 2*n - 2)/2), if(n%2==0, (n^2+n+2)^2/4, (n+1)*(n-1)*(n^3 + n^2 - 6*n + 6)/8))/4)} \\ Andrew Howroyd, Sep 09 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Apr 25 2012
STATUS
approved