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A290941 Number of dominating sets in the triangular honeycomb bishop graph. 2
1, 5, 45, 801, 27825, 1888509, 251530965, 66071455065, 34377356632185, 35547790276600245, 73223899601462711325, 300932502371711624263185, 2469959282065905379932069825, 40511383384524208761581247597165, 1328271546538715856399886647330605925 (list; graph; refs; listen; history; text; internal format)
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 A191962 A050641

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

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Last modified February 19 18:31 EST 2018. Contains 299356 sequences. (Running on oeis4.)