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A373395
Number of minimum connected dominating sets in the n-triangular graph.
2
1, 3, 12, 80, 750, 9072, 134456, 2359296, 47829690, 1100000000, 28295372292, 804925734912, 25090245516518, 850408685629440, 31139121093750000, 1224979098644774912, 51523614927176684274, 2307351090835290783744, 109607737155696043718780, 5505024000000000000000000
OFFSET
2,2
COMMENTS
For n > 2, the connected domination number of the n-triangular graph is n-2.
LINKS
Eric Weisstein's World of Mathematics, Connected Dominating Set.
Eric Weisstein's World of Mathematics, Triangular Graph.
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
MATHEMATICA
a[2] := 1; a[n_] := n*(n - 1)^(n - 3); Table[a[n], {n, 2, 19}] (* Detlef Meya, Jun 20 2024 *)
PROG
(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
(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
CROSSREFS
Sequence in context: A380028 A084565 A323634 * A275488 A304561 A303227
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jun 03 2024
EXTENSIONS
a(9) and beyond from Detlef Meya, Jun 20 2024
STATUS
approved