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A288183 Triangle read by rows: T(n,k) = number of arrangements of k non-attacking bishops on the black squares of an n X n board with every square controlled by at least one bishop.

%I A288183 #16 Feb 16 2025 08:33:47
%S A288183 2,1,4,0,4,4,0,0,22,8,0,0,16,64,8,0,0,6,128,228,16,0,0,0,72,784,528,
%T A288183 16,0,0,0,0,1056,4352,1688,32,0,0,0,0,432,9072,18336,3584,32,0,0,0,0,
%U A288183 120,7776,76488,87168,11024,64,0,0,0,0,0,2880,109152,484416,313856,22592,64
%N A288183 Triangle read by rows: T(n,k) = number of arrangements of k non-attacking bishops on the black squares of an n X n board with every square controlled by at least one bishop.
%C A288183 See A146304 for algorithm and PARI code to produce this sequence.
%C A288183 Equivalently, the coefficients of the maximal independent set polynomials on the n X n black bishop graph.
%C A288183 The product of the first nonzero term in each row of this sequence and that of A288182 give A122749.
%H A288183 Andrew Howroyd, <a href="/A288183/b288183.txt">Table of n, a(n) for n = 2..1276</a>
%H A288183 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BlackBishopGraph.html">Black Bishop Graph</a>
%H A288183 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximalIndependentVertexSet.html">Maximal Independent Vertex Set</a>
%e A288183 Triangle begins:
%e A288183   2;
%e A288183   1, 4;
%e A288183   0, 4,  4;
%e A288183   0, 0, 22,   8;
%e A288183   0, 0, 16,  64,    8;
%e A288183   0, 0,  6, 128,  228,   16;
%e A288183   0, 0,  0,  72,  784,  528,    16;
%e A288183   0, 0,  0,   0, 1056, 4352,  1688,    32;
%e A288183   0, 0,  0,   0,  432, 9072, 18336,  3584,    32;
%e A288183   0, 0,  0,   0,  120, 7776, 76488, 87168, 11024,  64;
%e A288183   ...
%e A288183 The first term is T(2,1) = 2.
%Y A288183 Row sums are A290594.
%Y A288183 Cf. A288182, A122749, A274105, A146304.
%K A288183 nonn,tabl
%O A288183 2,1
%A A288183 _Andrew Howroyd_, Jun 06 2017