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

2,1

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.

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

Example

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.

Crossrefs

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

Keyword

nonn,tabl

Author

Andrew Howroyd, Jun 06 2017

Status

approved