cp's OEIS Frontend

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

%I A289164 #9 Feb 16 2025 08:33:48
%S A289164 1,3,25,201,6979,233727,31262125,4103802933,2141080094839,
%T A289164 1107896230202475,2284899650399760961,4697484584102406799521,
%U A289164 38572957675399837886746123,316392839278535985537956881623,10375350180532286630209934837828053
%N A289164 Number of dominating sets in the n X n black bishop graph.
%H A289164 Andrew Howroyd, <a href="/A289164/b289164.txt">Table of n, a(n) for n = 1..50</a>
%H A289164 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BlackBishopGraph.html">Black Bishop Graph</a>
%H A289164 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominatingSet.html">Dominating Set</a>
%o A289164 (PARI)
%o A289164 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]}
%o A289164 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}
%o A289164 Bishop(n, white)=vector(n-if(white, n%2, 1-n%2), i, n-i+if(white, 1-i%2, i%2));
%o A289164 a(n)=DomSetCount(Bishop(n,0),1); \\ _Andrew Howroyd_, Nov 05 2017
%Y A289164 Cf. A286886, A289145, A289170.
%K A289164 nonn
%O A289164 1,2
%A A289164 _Eric W. Weisstein_, Jun 26 2017
%E A289164 Terms a(8) and beyond from _Andrew Howroyd_, Nov 05 2017