cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A298104 #11 Feb 16 2025 08:33:53
%S A298104 1,7,54,918,31072,2053184,266478640,68560228400,35159451505536,
%T A298104 36021118923496320,73782296097354062336,302225812400352055040512,
%U A298104 2475866621867539032536216576,40564755669895936890639118713856,1329227401230786888692092742930946048
%N A298104 Number of connected dominating sets in the n-triangular graph.
%H A298104 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedDominatingSet.html">Connected Dominating Set</a>
%H A298104 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JohnsonGraph.html">Johnson Graph</a>
%H A298104 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularGraph.html">Triangular Graph</a>
%F A298104 a(n) = A001187(n) + n*A001187(n-1) for n > 2. - _Andrew Howroyd_, Jan 14 2018
%t A298104 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 *)
%o A298104 (PARI)
%o A298104 b(n)={serlaplace(-x + log(sum(k=0, n, 2^binomial(k, 2)*x^k/k! + O(x*x^n))))}
%o A298104 { my(n=20); Vec(b(n) + x*deriv(x*b(n))) } \\ _Andrew Howroyd_, Jan 14 2018
%Y A298104 Cf. A001187, A290716, A290847.
%K A298104 nonn
%O A298104 2,2
%A A298104 _Eric W. Weisstein_, Jan 12 2018
%E A298104 a(8)-a(16) from _Andrew Howroyd_, Jan 14 2018