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A288182 Triangle read by rows: T(n,k) = number of arrangements of k non-attacking bishops on the white squares of an n X n board with every square controlled by at least one bishop (1<=k

%I A288182 #15 Feb 16 2025 08:33:47
%S A288182 2,0,2,0,4,4,0,2,16,4,0,0,16,64,8,0,0,0,128,160,8,0,0,0,72,784,528,16,
%T A288182 0,0,0,24,864,3672,1152,16,0,0,0,0,432,9072,18336,3584,32,0,0,0,0,0,
%U A288182 8304,65664,69472,7424,32,0,0,0,0,0,2880,109152,484416,313856,22592,64
%N A288182 Triangle read by rows: T(n,k) = number of arrangements of k non-attacking bishops on the white squares of an n X n board with every square controlled by at least one bishop (1<=k<n).
%C A288182 See A146304 for algorithm and PARI code to produce this sequence.
%C A288182 Equivalently, the coefficients of the maximal independent set polynomials on the n X n white bishop graph.
%C A288182 The product of the first nonzero term in each row of this sequence and that of A288183 give A122749.
%H A288182 Andrew Howroyd, <a href="/A288182/b288182.txt">Table of n, a(n) for n = 2..1276</a>
%H A288182 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximalIndependentVertexSet.html">Maximal Independent Vertex Set</a>
%H A288182 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WhiteBishopGraph.html">White Bishop Graph</a>
%e A288182 Triangle starts (first term is n=2, k=1):
%e A288182   2;
%e A288182   0, 2;
%e A288182   0, 4,  4;
%e A288182   0, 2, 16,   4;
%e A288182   0, 0, 16,  64,   8;
%e A288182   0, 0,  0, 128, 160,    8;
%e A288182   0, 0,  0,  72, 784,  528,    16;
%e A288182   0, 0,  0,  24, 864, 3672,  1152,    16;
%e A288182   0, 0,  0,   0, 432, 9072, 18336,  3584,   32;
%e A288182   0, 0,  0,   0,   0, 8304, 65664, 69472, 7424, 32;
%e A288182   ...
%Y A288182 Row sums are A290613.
%Y A288182 Cf. A288183, A122749, A274106, A146304.
%K A288182 nonn,tabl
%O A288182 2,1
%A A288182 _Andrew Howroyd_, Jun 06 2017