A235248 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 6, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

210, 906, 906, 3746, 3146, 3746, 16150, 10866, 10866, 16150, 66874, 41246, 31858, 41246, 66874, 288510, 152178, 108374, 108374, 152178, 288510, 1195458, 599342, 359962, 338282, 359962, 599342, 1195458, 5161934, 2282514, 1305758, 1039502

Offset

1,1

Comments

Table starts

210 906 3746 16150 66874 288510 1195458

906 3146 10866 41246 152178 599342 2282514

3746 10866 31858 108374 359962 1305758 4596034

16150 41246 108374 338282 1039502 3521538 11626526

66874 152178 359962 1039502 2965442 9463558 29462346

288510 599342 1305758 3521538 9463558 28726138 85432998

1195458 2282514 4596034 11626526 29462346 85432998 243061138

5161934 9184758 17276982 41097666 98737622 274327842 751070550

21400266 35696098 63001946 141434374 322636258 861350910 2271413066

92486622 145885710 243085134 515121002 1117067382 2864080130 7286424566

Links

R. H. Hardin, Table of n, a(n) for n = 1..143

Formula

Empirical for column k (the k=3..4 recurrence also works for k=1..2; apparently all rows and columns satisfy the same order 61 recurrence):

k=1: [linear recurrence of order 8].

k=2: [order 35].

k=3..4: [same order 61 recurrence].

Example

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

Crossrefs

Sequence in context: A163263 A009127 A158559 * A235241 A046302 A217532

Adjacent sequences: A235245 A235246 A235247 * A235249 A235250 A235251

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 05 2014

Status

approved