A235319 T(n,k) is the number of (n+1) X (k+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 7 (constant-stress 1 X 1 tilings).

112, 392, 392, 1120, 1120, 1120, 3920, 2744, 2744, 3920, 11776, 8392, 5968, 8392, 11776, 41216, 22568, 16352, 16352, 22568, 41216, 128128, 71896, 40144, 40144, 40144, 71896, 128128, 448448, 206360, 118160, 89600, 89600, 118160, 206360

Offset

1,1

Comments

Table starts

112 392 1120 3920 11776 41216 128128 448448

392 1120 2744 8392 22568 71896 206360 675064

1120 2744 5968 16352 40144 118160 316912 978320

3920 8392 16352 40144 89600 241600 598976 1723456

11776 22568 40144 89600 184144 459536 1062832 2873552

41216 71896 118160 241600 459536 1062832 2291696 5805424

128128 206360 316912 598976 1062832 2291696 4632208 11046512

448448 675064 978320 1723456 2873552 5805424 11046512 24862768

1426432 2026472 2793040 4616960 7275856 13828496 24862768 52954448

4992512 6751000 8912144 13917952 20859728 37480816 63985520 129456304

Empirical: T(n,k) is the number of (n+1) X (k+1) 0..5+i arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 5+2*i (constant-stress 1 X 1 tilings), for i=1..3(..?).

Links

R. H. Hardin, Table of n, a(n) for n = 1..260

Formula

Empirical for column k (the k=2..6 recurrence also works for k=1; apparently all rows and columns satisfy the same order 18 recurrence):

k=1: a(n) = 28*a(n-2) - 252*a(n-4) + 720*a(n-6).

k=2..6: [same order 18 recurrence]

Example

Some solutions for n=4, k=4:
  5 4 6 1 5    2 4 2 4 2    1 6 2 4 2    3 0 3 0 3
  0 6 1 3 0    6 1 6 1 6    4 2 5 0 5    1 5 1 5 1
  4 3 5 0 4    3 5 3 5 3    0 5 1 3 1    5 2 5 2 5
  0 6 1 3 0    5 0 5 0 5    4 2 5 0 5    2 6 2 6 2
  4 3 5 0 4    2 4 2 4 2    1 6 2 4 2    3 0 3 0 3

Crossrefs

Sequence in context: A352585 A233892 A233885 * A203923 A235312 A203916

Adjacent sequences: A235316 A235317 A235318 * A235320 A235321 A235322

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 05 2014

Status

approved