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

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..50

Eric Weisstein's World of Mathematics, Dominating Set

Prog

(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

Crossrefs

Cf. A290875 (minimal dominating sets).

Sequence in context: A167812 A155104 A243951 * A211051 A322661 A191962

Adjacent sequences: A290938 A290939 A290940 * A290942 A290943 A290944

Keyword

nonn

Author

Eric W. Weisstein, Aug 14 2017

Extensions

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

Status

approved