A290941 Number of dominating sets in the triangular honeycomb bishop graph.
1, 5, 45, 801, 27825, 1888509, 251530965, 66071455065, 34377356632185, 35547790276600245, 73223899601462711325, 300932502371711624263185, 2469959282065905379932069825, 40511383384524208761581247597165, 1328271546538715856399886647330605925
Offset: 1
Keywords
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..50
- Eric Weisstein's World of Mathematics, Dominating Set
Crossrefs
Cf. A290875 (minimal dominating sets).
Programs
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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} a(n)=DomSetCount(Vecrev([1..n]),1); \\ Andrew Howroyd, Nov 05 2017
Extensions
Terms a(8) and beyond from Andrew Howroyd, Nov 05 2017