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 A303212 #27 Jun 11 2025 18:33:36
%S A303212 0,1,6,96,600,2400,7350,18816,42336,86400,163350,290400,490776,794976,
%T A303212 1242150,1881600,2774400,3995136,5633766,7797600,10613400,14229600,
%U A303212 18818646,24579456,31740000,40560000,51333750,64393056,80110296,98901600
%N A303212 Number of minimum total dominating sets in the n X n rook complement graph.
%C A303212 For n > 2, the minimum total dominating sets are any three vertices such that no two are in the same row or column. - _Andrew Howroyd_, Apr 20 2018
%C A303212 Essentially the same as A179058(n), differing only for n=2. - _Eric W. Weisstein_, Dec 06 2023
%H A303212 Colin Barker, <a href="/A303212/b303212.txt">Table of n, a(n) for n = 1..1000</a>
%H A303212 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>.
%H A303212 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimumTotalDominatingSet.html">Minimum Total Dominating Set</a>.
%H A303212 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A303212 a(n) = A179058(n) for n > 2. - _Andrew Howroyd_, Apr 20 2018
%F A303212 From _Colin Barker_, Apr 20 2018: (Start)
%F A303212 G.f.: x^2*(1 - x + 75*x^2 + 19*x^3 + 41*x^4 - 21*x^5 + 7*x^6 - x^7) / (1 - x)^7.
%F A303212 a(n) = n^2*(2 - 3*n + n^2)^2 / 6 for n > 2.
%F A303212 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 9.
%F A303212 (End)
%t A303212 Table[If[n == 2, 1, 6 Binomial[n, 3]^2], {n, 20}]
%t A303212 Join[{0, 1}, LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 6, 96, 600, 2400, 7350}, {3, 20}]]
%t A303212 CoefficientList[Series[x (-1 + x - 75 x^2 - 19 x^3 - 41 x^4 + 21 x^5 - 7 x^6 + x^7)/(-1 + x)^7, {x, 0, 20}], x]
%o A303212 (PARI) a(n) = if(n<3, n==2, 6*binomial(n,3)^2) \\ _Andrew Howroyd_, Apr 20 2018
%o A303212 (PARI) concat(0, Vec(x^2*(1 - x + 75*x^2 + 19*x^3 + 41*x^4 - 21*x^5 + 7*x^6 - x^7) / (1 - x)^7 + O(x^60))) \\ _Colin Barker_, Apr 20 2018
%Y A303212 Cf. A179058, A303209, A347922.
%K A303212 nonn,easy
%O A303212 1,3
%A A303212 _Eric W. Weisstein_, Apr 19 2018
%E A303212 a(6)-a(30) from _Andrew Howroyd_, Apr 20 2018