A289164 Number of dominating sets in the n X n black bishop graph.

1, 3, 25, 201, 6979, 233727, 31262125, 4103802933, 2141080094839, 1107896230202475, 2284899650399760961, 4697484584102406799521, 38572957675399837886746123, 316392839278535985537956881623, 10375350180532286630209934837828053

Offset: 1

Author

Eric W. Weisstein, Jun 26 2017

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..50
• Eric Weisstein's World of Mathematics, Black Bishop Graph
• Eric Weisstein's World of Mathematics, Dominating Set

Crossrefs

Cf. A286886, A289145, A289170.

Programs

PARI

Collect(sig,v,r,x)={forstep(r=r, 1, -1, my(w=sig[r]+1); v=vector(#v, k, sum(j=1, k, binomial(#v-j,k-j)*v[j]*x^(k-j)*(1+x)^(w-#v+j-1))-v[k])); v[#v]}
DomSetCount(sig,x)={my(v=[1]); my(total=Collect(sig,v,#sig,x)); forstep(r=#sig, 1, -1, my(w=sig[r]+1); total+=Collect(sig, vector(w,k,if(k<=#v,v[k])), r-1, x); v=vector(w, k, sum(j=1, min(k,#v), binomial(w-j, k-j)*v[j]*x^(k-j)*(1+x)^(j-1)))); total}
Bishop(n, white)=vector(n-if(white, n%2, 1-n%2), i, n-i+if(white, 1-i%2, i%2));
a(n)=DomSetCount(Bishop(n,0),1); \\ Andrew Howroyd, Nov 05 2017

Extensions

Terms a(8) and beyond from Andrew Howroyd, Nov 05 2017