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.
%I A347922 #16 Feb 16 2025 08:34:02
%S A347922 0,1,51,492,2500,8925,25431,61936,134352,266625,493075,861036,1433796,
%T A347922 2293837,3546375,5323200,7786816,11134881,15604947,21479500,29091300,
%U A347922 38829021,51143191,66552432,85650000,109110625,137697651,172270476,213792292,263338125
%N A347922 Number of minimal total dominating sets in the n X n rook complement graph.
%C A347922 From _Andrew Howroyd_, Jan 19 2022: (Start)
%C A347922 The vertex sets which are not totally dominating are just those that are contained in the union of a single row and column. Minimal total dominating sets are:
%C A347922 - any three vertices such that no two are in the same row or column,
%C A347922 - two vertices in each of two rows/columns. (End)
%H A347922 Andrew Howroyd, <a href="/A347922/b347922.txt">Table of n, a(n) for n = 1..1000</a>
%H A347922 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalTotalDominatingSet.html">Minimal Total Dominating Set</a>
%H A347922 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>
%H A347922 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A347922 From _Andrew Howroyd_, Jan 19 2022: (Start)
%F A347922 a(n) = 6*binomial(n,3)^2 + 2*binomial(n,2)^3 - binomial(n,2)^2.
%F A347922 a(n) = (5*n^2 - 11*n + 5)*n^2*(n-1)^2/12.
%F A347922 G.f.: x*(1 + 44*x + 156*x^2 + 92*x^3 + 7*x^4)/(1 - x)^7.
%F A347922 (End)
%t A347922 Table[(n - 1)^2 n^2 (5 n^2 - 11 n + 5)/12, {n, 20}] (* _Eric W. Weisstein_, May 11 2024 *)
%t A347922 LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 1, 51, 492, 2500, 8925, 25431}, 20] (* _Eric W. Weisstein_, May 11 2024 *)
%t A347922 CoefficientList[Series[-x (1 + 44 x + 156 x^2 + 92 x^3 + 7 x^4)/(-1 + x)^7, {x, 0, 20}], x] (* _Eric W. Weisstein_, May 11 2024 *)
%o A347922 (PARI) a(n) = (5*n^2 - 11*n + 5)*n^2*(n-1)^2/12 \\ _Andrew Howroyd_, Jan 19 2022
%Y A347922 Cf. A292074, A303209, A303212.
%K A347922 nonn,easy
%O A347922 1,3
%A A347922 _Eric W. Weisstein_, Sep 19 2021
%E A347922 Terms a(6) and beyond from _Andrew Howroyd_, Jan 19 2022