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

0,4

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, Total Dominating Set

Eric Weisstein's World of Mathematics, Triangular Graph

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

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 *)

Prog

(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

Crossrefs

Cf. A290716, A303048, A304561.

Sequence in context: A323634 A275488 A304561 * A182166 A303047 A197445

Adjacent sequences: A303224 A303225 A303226 * A303228 A303229 A303230

Keyword

nonn

Author

Eric W. Weisstein, Apr 20 2018

Extensions

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

Status

approved