A298104 Number of connected dominating sets in the n-triangular graph.

1, 7, 54, 918, 31072, 2053184, 266478640, 68560228400, 35159451505536, 36021118923496320, 73782296097354062336, 302225812400352055040512, 2475866621867539032536216576, 40564755669895936890639118713856, 1329227401230786888692092742930946048

Offset: 2

Author

Eric W. Weisstein, Jan 12 2018

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Connected Dominating Set
• Eric Weisstein's World of Mathematics, Johnson Graph
• Eric Weisstein's World of Mathematics, Triangular Graph

Crossrefs

Cf. A001187, A290716, A290847.

Programs

Mathematica

a[n_] := a[n] = 2^Binomial[n, 2] - Sum[k Binomial[n, k] 2^((n - k) (n - k - 1)/2) a[k], {k, n - 1}]/n; Join[{1}, Table[a[n] + n a[n - 1], {n, 3, 20}]] (* Eric W. Weisstein, Jan 15 2018 *)

PARI

b(n)={serlaplace(-x + log(sum(k=0, n, 2^binomial(k, 2)*x^k/k! + O(x*x^n))))}
{ my(n=20); Vec(b(n) + x*deriv(x*b(n))) } \\ Andrew Howroyd, Jan 14 2018

Formula

a(n) = A001187(n) + n*A001187(n-1) for n > 2. - Andrew Howroyd, Jan 14 2018

Extensions

a(8)-a(16) from Andrew Howroyd, Jan 14 2018