A303227 Number of minimal total dominating sets in the n-triangular (Johnson) graph.

1, 1, 0, 3, 12, 80, 840, 4032, 31976, 371016, 4354650, 55066880, 680003412, 9047989392, 132626606294, 2096065474440, 34991505975120, 607163217989312, 11006996786618994, 209218563659672064, 4168806234781798100, 86745911047924139760, 1876774293382882814382

Offset: 0

Author

Eric W. Weisstein, Apr 20 2018

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• Eric Weisstein's World of Mathematics, Johnson Graph.
• Eric Weisstein's World of Mathematics, Minimal Total Dominating Set.
• Eric Weisstein's World of Mathematics, Triangular Graph.

Crossrefs

Cf. A290716, A303048, A304561.

Programs

Mathematica

Range[0, 20]! CoefficientList[Series[Exp[x^3/2] + x Exp[x Exp[x^2 + x] - (x + x^2 + x^3 + x^4/2)], {x, 0, 20}], x] (* Eric W. Weisstein, Apr 23 2018 *)

PARI

seq(n)={Vec(serlaplace(exp(x^3/2 + O(x*x^n)) + x*exp(x*exp(x^2+x + O(x^n)) - (x+x^2+x^3+x^4/2))))} \\ Andrew Howroyd, Apr 21 2018

Formula

E.g.f.: exp(x^3/2) + x*exp(x*exp(x^2+x) - (x+x^2+x^3+x^4/2)). - Andrew Howroyd, Apr 21 2018

Extensions

a(0)-a(1) prepended and a(8)-a(22) from Andrew Howroyd, Apr 21 2018