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A288183
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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.
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5
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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, 16, 0, 0, 0, 0, 1056, 4352, 1688, 32, 0, 0, 0, 0, 432, 9072, 18336, 3584, 32, 0, 0, 0, 0, 120, 7776, 76488, 87168, 11024, 64, 0, 0, 0, 0, 0, 2880, 109152, 484416, 313856, 22592, 64
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OFFSET
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2,1
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COMMENTS
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See A146304 for algorithm and PARI code to produce this sequence.
Equivalently, the coefficients of the maximal independent set polynomials on the n X n black bishop graph.
The product of the first nonzero term in each row of this sequence and that of A288182 give A122749.
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 2..1276
Eric Weisstein's World of Mathematics, Black Bishop Graph
Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set
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EXAMPLE
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Triangle begins:
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, 16;
0, 0, 0, 0, 1056, 4352, 1688, 32;
0, 0, 0, 0, 432, 9072, 18336, 3584, 32;
0, 0, 0, 0, 120, 7776, 76488, 87168, 11024, 64;
...
The first term is T(2,1) = 2.
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CROSSREFS
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Row sums are A290594.
Cf. A288182, A122749, A274105, A146304.
Sequence in context: A059781 A233905 A285284 * A324055 A087664 A158032
Adjacent sequences: A288180 A288181 A288182 * A288184 A288185 A288186
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KEYWORD
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nonn,tabl
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AUTHOR
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Andrew Howroyd, Jun 06 2017
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STATUS
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approved
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