A373395 Number of minimum connected dominating sets in the n-triangular graph.

1, 3, 12, 80, 750, 9072, 134456, 2359296, 47829690, 1100000000, 28295372292, 804925734912, 25090245516518, 850408685629440, 31139121093750000, 1224979098644774912, 51523614927176684274, 2307351090835290783744, 109607737155696043718780, 5505024000000000000000000

Offset: 2

Author

Eric W. Weisstein, Jun 03 2024

Keywords

• nonn

Comments

For n > 2, the connected domination number of the n-triangular graph is n-2.

Links

• G. C. Greubel, Table of n, a(n) for n = 2..385
• Eric Weisstein's World of Mathematics, Connected Dominating Set.
• Eric Weisstein's World of Mathematics, Triangular Graph.

Programs

Magma

A373395:= func< n | n eq 2 select 1 else n*(n-1)^(n-3) >;
[A373395(n): n in [2..30]]; // G. C. Greubel, Mar 19 2025

Mathematica

a[2] := 1; a[n_] := n*(n - 1)^(n - 3); Table[a[n], {n, 2, 19}] (* Detlef Meya, Jun 20 2024 *)

SageMath

def A373395(n): return 1 if n==2 else n*(n-1)^(n-3)
print([A373395(n) for n in range(2,31)]) # G. C. Greubel, Mar 19 2025

Formula

a(2) = 1, a(n) = n*(n - 1)^(n - 3). - Detlef Meya, Jun 20 2024

E.g.f.: -(x/2)*((W(-x) + 1)^2 - 1 + x), where W(x) = Lambert W function. - G. C. Greubel, Mar 19 2025

Extensions

a(9) and beyond from Detlef Meya, Jun 20 2024