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 A291623 #21 Feb 16 2025 08:33:50
%S A291623 1,4,48,320,1610,6012,17948,45488,101970,207920,393272,699888,1184378,
%T A291623 1921220,3006180,4560032,6732578,9706968,13704320,18988640,25872042,
%U A291623 34720268,45958508,60077520,77640050,99287552,125747208,157839248,196484570,242712660
%N A291623 Number of maximal irredundant and minimal dominating sets in the n X n rook complement graph.
%C A291623 From _Andrew Howroyd_, Aug 30 2017: (Start)
%C A291623 For n > 2 the maximal irredundant sets are:
%C A291623 - all vertices in any single row or column,
%C A291623 - any three vertices such that no two are in the same row or column,
%C A291623 - any vertex with another in the same row and a third in the same column,
%C A291623 - two vertices in each of two rows/columns and none in the same column/row. (End)
%H A291623 Andrew Howroyd, <a href="/A291623/b291623.txt">Table of n, a(n) for n = 1..500</a>
%H A291623 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximalIrredundantSet.html">Maximal Irredundant Set</a>
%H A291623 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalDominatingSet.html">Minimal Dominating Set</a>
%H A291623 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>
%H A291623 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F A291623 From _Andrew Howroyd_, Aug 30 2017: (Start)
%F A291623 a(n) = 2*n + 6*binomial(n,3)^2 + n^2*(n-1)^2 + 12*binomial(n,4)*binomial(n,2) for n > 2.
%F A291623 a(n) = (5*n^6 - 33*n^5 + 89*n^4 - 99*n^3 + 38*n^2 + 24*n) / 12 for n > 2.
%F A291623 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 A291623 G.f.: x*(1 - 3*x + 41*x^2 + 33*x^3 + 273*x^4 - 99*x^5 + 77*x^6 - 27*x^7 + 4*x^8)/(1-x)^7.
%F A291623 (End)
%t A291623 Table[Piecewise[{{1, n == 1}, {4, n == 2}}, 2 n + 6 Binomial[n, 3]^2 + n^2 (n - 1)^2 + 12 Binomial[n, 4] Binomial[n, 2]], {n, 20}]
%t A291623 Join[{1, 4}, LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {48, 320, 1610, 6012, 17948, 45488, 101970}, 18]]
%t A291623 CoefficientList[Series[(-1 + 3 x - 41 x^2 - 33 x^3 - 273 x^4 + 99 x^5 - 77 x^6 + 27 x^7 - 4 x^8)/(-1 + x)^7, {x, 0, 20}], x]
%o A291623 (PARI) a(n) = if(n<3, [1,4][n], (5*n^6 - 33*n^5 + 89*n^4 - 99*n^3 + 38*n^2 + 24*n) / 12); \\ _Andrew Howroyd_, Aug 30 2017
%Y A291623 Cf. A291622.
%K A291623 nonn
%O A291623 1,2
%A A291623 _Eric W. Weisstein_, Aug 28 2017
%E A291623 Terms a(6) and beyond from _Andrew Howroyd_, Aug 30 2017