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A298104
Number of connected dominating sets in the n-triangular graph.
2
1, 7, 54, 918, 31072, 2053184, 266478640, 68560228400, 35159451505536, 36021118923496320, 73782296097354062336, 302225812400352055040512, 2475866621867539032536216576, 40564755669895936890639118713856, 1329227401230786888692092742930946048
OFFSET
2,2
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
FORMULA
a(n) = A001187(n) + n*A001187(n-1) for n > 2. - Andrew Howroyd, Jan 14 2018
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jan 12 2018
EXTENSIONS
a(8)-a(16) from Andrew Howroyd, Jan 14 2018
STATUS
approved