cp's OEIS Frontend

A288958 Number of cliques in the n X n rook graph.

%I A288958 #21 May 22 2025 21:00:16
%S A288958 1,2,9,34,105,286,721,1730,4017,9118,20361,44914,98137,212798,458529,
%T A288958 982786,2096865,4456126,9436825,19922546,41942601,88079902,184548849,
%U A288958 385875394,805305745,1677720926,3489660201,7247756530,15032384697,31138511998,64424508481
%N A288958 Number of cliques in the n X n rook graph.
%C A288958 Also the number of independent vertex sets in the n X n rook complement graph. - _Eric W. Weisstein_, Sep 11 2017
%H A288958 Andrew Howroyd, <a href="/A288958/b288958.txt">Table of n, a(n) for n = 0..1000</a>
%H A288958 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Clique.html">Clique</a>
%H A288958 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependentVertexSet.html">Independent Vertex Set</a>
%H A288958 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>
%H A288958 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookGraph.html">Rook Graph</a>
%H A288958 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (7,-19,25,-16,4).
%F A288958 a(n) = 1 + 2*n*(2^n - 1) - n^2.
%F A288958 a(n) = 7*a(n-1) - 19*a(n-2) + 25*a(n-3) - 16*a(n-4) + 4*a(n-5).
%F A288958 G.f.: (1 - 5*x + 14*x^2 - 16*x^3 + 4*x^4)/((1 - x)^3*(1 - 2*x)^2).
%t A288958 LinearRecurrence[{7, -19, 25, -16, 4}, {2, 9, 34, 105, 286}, 20]
%t A288958 Table[1 + 2 n (2^n - 1) - n^2, {n, 20}]
%t A288958 CoefficientList[Series[(2 - 5 x + 9 x^2 - 12 x^3 + 4 x^4)/((1 - x)^3 (1 - 2 x)^2), {x, 0, 20}], x]
%Y A288958 Main diagonal of A384120.
%K A288958 nonn,easy
%O A288958 0,2
%A A288958 _Eric W. Weisstein_, Jun 20 2017
%E A288958 a(0) = 1 prepended by _Andrew Howroyd_, May 22 2025