A234728 T(n,k) is the number of (n+1) X (k+1) 0..7 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 7 (constant-stress 1 X 1 tilings).

240, 1096, 1096, 4192, 3976, 4192, 19120, 12464, 12464, 19120, 74496, 48976, 33560, 48976, 74496, 339328, 168928, 116168, 116168, 168928, 339328, 1344640, 692512, 360760, 357208, 360760, 692512, 1344640, 6116416, 2531888, 1349336, 1000264

Offset

1,1

Comments

Table starts

240 1096 4192 19120 74496 339328 1344640

1096 3976 12464 48976 168928 692512 2531888

4192 12464 33560 116168 360760 1349336 4577624

19120 48976 116168 357208 1000264 3403528 10632200

74496 168928 360760 1000264 2557656 8002936 23194936

339328 692512 1349336 3403528 8002936 23137720 62379416

1344640 2531888 4577624 10632200 23194936 62379416 157274648

6116416 10649920 17961560 38594056 78550072 197412088 467509400

24606720 40456096 64580152 129877960 248588376 587074168 1311421240

111778816 173104096 261840344 493469896 891039928 1982807032 4191830168

Links

R. H. Hardin, Table of n, a(n) for n = 1..159

Formula

Empirical for column k (k=2 recurrence also works for k=1; apparently all rows and columns satisfy the same order 30 recurrence):

k=1: a(n) = 68*a(n-2) -1724*a(n-4) +19312*a(n-6) -80640*a(n-8).

k=2..5: [same order 30 recurrence].

Example

Some solutions for n=3, k=4:
  0 3 1 3 0      2 7 2 7 2      6 0 5 0 4      0 5 1 6 1
  5 1 6 1 5      3 1 3 1 3      4 5 3 5 2      6 4 7 5 7
  4 7 5 7 4      1 6 1 6 1      6 0 5 0 4      0 5 1 6 1
  5 1 6 1 5      5 3 5 3 5      3 4 2 4 1      4 2 5 3 5

Crossrefs

Sequence in context: A092000 A124352 A158562 * A234721 A235212 A235205

Adjacent sequences: A234725 A234726 A234727 * A234729 A234730 A234731

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 30 2013

Status

approved