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 A292074 #22 Feb 16 2025 08:33:51
%S A292074 1,4,48,240,1000,3300,9114,21952,47520,94500,175450,307824,515112,
%T A292074 828100,1286250,1939200,2848384,4088772,5750730,7942000,10789800,
%U A292074 14443044,19074682,24884160,32100000,40982500,51826554,64964592,80769640,99658500,122095050
%N A292074 Number of minimum dominating sets in the n X n rook complement graph.
%C A292074 The minimum dominating sets are the minimal dominating sets (A291623) of size equal to the domination number. For n > 2, the domination number is 3. For n > 3, the minimal dominating sets of size 3 are either any three vertices such that no two are in the same row or column or any vertex with another in the same row and a third in the same column. For n = 3, the case of all vertices in a single row or column also needs to be included. - _Andrew Howroyd_, Sep 13 2017
%H A292074 Andrew Howroyd, <a href="/A292074/b292074.txt">Table of n, a(n) for n = 1..200</a>
%H A292074 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimumDominatingSet.html">Minimum Dominating Set</a>
%H A292074 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>
%H A292074 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A292074 G.f.: x*(-1 + 3*x - 41*x^2 + 47*x^3 - 223*x^4 + 221*x^5 - 217*x^6 + 127*x^7 - 42*x^8 + 6*x^9)/(-1 + x)^7.
%F A292074 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 > 10.
%F A292074 a(n) = 6*binomial(n, 3)^2 + n^2*(n-1)^2 for n > 3. - _Andrew Howroyd_, Sep 13 2017
%t A292074 Join[{1, 4, 48}, LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {240, 1000, 3300, 9114, 21952, 47520, 94500}, 20]]
%t A292074 Table[Piecewise[{{1, n == 1}, {48, n == 3}}, 6 Binomial[n, 3]^2 + n^2 (n - 1)^2], {n, 20}]
%t A292074 CoefficientList[Series[(-1 + 3 x - 41 x^2 + 47 x^3 - 223 x^4 + 221 x^5 - 217 x^6 + 127 x^7 - 42 x^8 + 6 x^9)/(-1 + x)^7, {x, 0, 20}], x]
%o A292074 (PARI) a(n) = if(n<4, [1,4,48][n], 6*binomial(n, 3)^2 + n^2*(n-1)^2); \\ _Andrew Howroyd_, Sep 13 2017
%Y A292074 Cf. A291623, A292073.
%K A292074 nonn,easy
%O A292074 1,2
%A A292074 _Eric W. Weisstein_, Sep 12 2017
%E A292074 Terms a(6) and beyond from _Andrew Howroyd_, Sep 13 2017