A289170 - OEIS

%I #8 Nov 05 2017 18:56:27

%S 3,11,201,3413,233727,15544607,4103802933,1069035156713,

%T 1107896230202475,1142044772648964275,4697484584102406799521,

%U 19284763179499969013836925,316392839278535985537956881623,5187559573137612606140331666573383

%N Number of dominating sets in the n X n white bishop graph.

%H Andrew Howroyd, <a href="/A289170/b289170.txt">Table of n, a(n) for n = 2..50</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DominatingSet.html">Dominating Set</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WhiteBishopGraph.html">White Bishop Graph</a>

%o (PARI)

%o 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 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 Bishop(n, white)=vector(n-if(white, n%2, 1-n%2), i, n-i+if(white, 1-i%2, i%2));

%o a(n)=DomSetCount(Bishop(n,1),1); \\ _Andrew Howroyd_, Nov 05 2017

%Y Cf. A287897, A289169, A289164.

%K nonn

%O 2,1

%A _Eric W. Weisstein_, Jun 26 2017

%E Terms a(8) and beyond from _Andrew Howroyd_, Nov 05 2017