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).

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, 0, 0, 0, 24, 864, 3672, 1152, 16, 0, 0, 0, 0, 432, 9072, 18336, 3584, 32, 0, 0, 0, 0, 0, 8304, 65664, 69472, 7424, 32, 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 white bishop graph.

The product of the first nonzero term in each row of this sequence and that of A288183 give A122749.

Links

Andrew Howroyd, Table of n, a(n) for n = 2..1276

Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set

Eric Weisstein's World of Mathematics, White Bishop Graph

Example

Triangle starts (first term is n=2, k=1):
  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;
  0, 0,  0,  24, 864, 3672,  1152,    16;
  0, 0,  0,   0, 432, 9072, 18336,  3584,   32;
  0, 0,  0,   0,   0, 8304, 65664, 69472, 7424, 32;
  ...

Crossrefs

Row sums are A290613.

Cf. A288183, A122749, A274106, A146304.

Sequence in context: A029186 A283023 A372554 * A072680 A067770 A079200

Adjacent sequences: A288179 A288180 A288181 * A288183 A288184 A288185

Keyword

nonn,tabl

Author

Andrew Howroyd, Jun 06 2017

Status

approved