A234681 T(n,k) is the number of (n+1) X (k+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 5 (constant-stress 1 X 1 tilings).

112, 404, 404, 1264, 1152, 1264, 4568, 2924, 2924, 4568, 14368, 9108, 6328, 9108, 14368, 52016, 25292, 17312, 17312, 25292, 52016, 164416, 82956, 43240, 41832, 43240, 82956, 164416, 596192, 243164, 129848, 93680, 93680, 129848, 243164

Offset

1,1

Comments

Table starts

112 404 1264 4568 14368 52016 164416 596192

404 1152 2924 9108 25292 82956 243164 823836

1264 2924 6328 17312 43240 129848 354856 1129256

4568 9108 17312 41832 93680 254784 639440 1878960

14368 25292 43240 93680 191128 476648 1109272 3039128

52016 82956 129848 254784 476648 1092120 2354408 5995464

164416 243164 354856 639440 1109272 2354408 4736536 11294552

596192 823836 1129256 1878960 3039128 5995464 11294552 25287288

1892992 2495084 3265864 5098448 7775608 14369096 25494136 53827832

6874304 8636892 10806344 15829008 22805432 39500136 66161144 132005016

Links

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

Formula

Empirical for column k (the k=2..7 order 18 recurrence also works for k=1; apparently all rows and columns satisfy the same order 18 recurrence):

k=1: a(n) = 22*a(n-2) -120*a(n-4).

k=2..7: [same order 18 recurrence].

Example

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

Crossrefs

Sequence in context: A203923 A235312 A203916 * A234674 A217992 A221798

Adjacent sequences: A234678 A234679 A234680 * A234682 A234683 A234684

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 29 2013

Status

approved