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 A291622 #18 Feb 16 2025 08:33:50
%S A291622 2,9,94,777,3286,10771,29366,69873,149950,297111,553114,980953,
%T A291622 1677014,2793771,4584286,7492065,12335422,20688751,35673698,63602601,
%U A291622 117391702,223644675,437338630,872239057,1763820926,3599298951,7386070186,15205369593,31353128470
%N A291622 Number of irredundant sets in the n X n rook complement graph.
%C A291622 The irredundant sets are the distinct subsets of the maximal irredundant sets. These are either any subset of vertices in a single row or column or otherwise have cardinality of at most four (see A291623). - _Andrew Howroyd_, Aug 30 2017
%H A291622 Andrew Howroyd, <a href="/A291622/b291622.txt">Table of n, a(n) for n = 1..200</a>
%H A291622 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IrredundantSet.html">Irredundant Set</a>
%H A291622 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>
%H A291622 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (11, -53, 147, -259, 301, -231, 113, -32, 4).
%F A291622 From _Andrew Howroyd_, Aug 30 2017: (Start)
%F A291622 a(n) = 2*n*(2^n) + (5*n^6 - 21*n^5 + 47*n^4 - 51*n^3 + 8*n^2 - 24*n + 12)/12 for n > 3.
%F A291622 a(n) = 11*a(n-1) - 53*a(n-2) + 147*a(n-3) - 259*a(n-4) + 301*a(n-5) - 231*a(n-6) + 113*a(n-7) - 32*a(n-8) + 4*a(n-9) for n > 12.
%F A291622 G.f.: x*(2 - 13*x + 101*x^2 - 74*x^3 - 1084*x^4 + 3717*x^5 - 7077*x^6 + 9470*x^7 - 7634*x^8 + 3876*x^9 - 1128*x^10 + 144*x^11)/((1 - x)^7*(1 - 2*x)^2).
%F A291622 (End)
%t A291622 Table[Piecewise[{{9, n == 2}, {94, n == 3}}, 2 n (2^n) + (5 n^6 - 21 n^5 + 47 n^4 - 51 n^3 + 8 n^2 - 24 n + 12)/12], {n, 20}]
%t A291622 Join[{2, 9, 94}, LinearRecurrence[{11, -53, 147, -259, 301, -231, 113, -32, 4}, {777, 3286, 10771, 29366, 69873, 149950, 297111, 553114, 980953}, 20]]
%t A291622 CoefficientList[Series[(2 - 13 x + 101 x^2 - 74 x^3 - 1084 x^4 + 3717 x^5 - 7077 x^6 + 9470 x^7 - 7634 x^8 + 3876 x^9 - 1128 x^10 + 144 x^11)/((1 - x)^7 (1 - 2 x)^2), {x, 0, 20}], x]
%o A291622 (PARI) a(n) = if(n<4, [2, 9, 94][n], 2*n*(2^n) + (5*n^6 - 21*n^5 + 47*n^4 - 51*n^3 + 8*n^2 - 24*n + 12)/12); \\ _Andrew Howroyd_, Aug 30 2017
%Y A291622 Cf. A291623.
%K A291622 nonn
%O A291622 1,1
%A A291622 _Eric W. Weisstein_, Aug 28 2017
%E A291622 Terms a(6) and beyond from _Andrew Howroyd_, Aug 30 2017