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.

A287065 Number of dominating sets on the n X n rook graph.

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%I A287065 #19 Feb 16 2025 08:33:46
%S A287065 1,11,421,59747,32260381,67680006971,559876911043381,
%T A287065 18412604442711949187,2416403019417984915336061,
%U A287065 1267413006543912045144741284411,2658304092145691708492995820522716981,22300364428188338185156192161829091442585827
%N A287065 Number of dominating sets on the n X n rook graph.
%C A287065 Number of {0,1} n X n matrices with no zero rows or no zero columns. - _Geoffrey Critzer_, Jan 15 2024
%H A287065 Andrew Howroyd, <a href="/A287065/b287065.txt">Table of n, a(n) for n = 1..50</a>
%H A287065 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominatingSet.html">Dominating Set</a>
%H A287065 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookGraph.html">Rook Graph</a>
%F A287065 a(n) = (2^n-1)^n + Sum_{i=1..n-1} binomial(n,i) * A183109(n,i). - _Andrew Howroyd_, May 22 2017
%t A287065 Table[(2^n - 1)^n + Sum[Binomial[n, i] Sum[(-1)^j (-1 + 2^(n - j))^i Binomial[n, j], {j, 0, n}], {i, n - 1}], {n, 20}] (* _Eric W. Weisstein_, May 27 2017 *)
%o A287065 (PARI)
%o A287065 b(m,n)=sum(j=0, m, (-1)^j*binomial(m, j)*(2^(m - j) - 1)^n);
%o A287065 a(n)=(2^n-1)^n + sum(i=1,n-1,b(n,i)*binomial(n,i)); \\ _Andrew Howroyd_, May 22 2017
%Y A287065 Main diagonal of A287274.
%Y A287065 Row sums of A368831.
%Y A287065 Cf. A183109, A002720, A048291, A173403.
%K A287065 nonn
%O A287065 1,2
%A A287065 _Eric W. Weisstein_, May 19 2017
%E A287065 a(6)-a(12) from _Andrew Howroyd_, May 22 2017