A290941 - OEIS

%I #10 Feb 16 2025 08:33:50

%S 1,5,45,801,27825,1888509,251530965,66071455065,34377356632185,

%T 35547790276600245,73223899601462711325,300932502371711624263185,

%U 2469959282065905379932069825,40511383384524208761581247597165,1328271546538715856399886647330605925

%N Number of dominating sets in the triangular honeycomb bishop graph.

%H Andrew Howroyd, <a href="/A290941/b290941.txt">Table of n, a(n) for n = 1..50</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominatingSet.html">Dominating Set</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 a(n)=DomSetCount(Vecrev([1..n]),1); \\ _Andrew Howroyd_, Nov 05 2017

%Y Cf. A290875 (minimal dominating sets).

%K nonn

%O 1,2

%A _Eric W. Weisstein_, Aug 14 2017

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