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.

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

Offset: 2

Author

Andrew Howroyd, Jun 06 2017

Keywords

• nonn
• tabl

Comments

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.

Examples

			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.
		

Links

• 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

Crossrefs

Row sums are A290594.

Cf. A288182, A122749, A274105, A146304.