A234712 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 (constant-stress 1 X 1 tilings).

322, 1730, 1730, 8738, 7154, 8738, 47306, 28170, 28170, 47306, 239890, 127586, 87698, 127586, 239890, 1308890, 546362, 334938, 334938, 546362, 1308890, 6664130, 2630882, 1224482, 1108418, 1224482, 2630882, 6664130, 36647114, 11903466

Offset

1,1

Comments

Table starts

322 1730 8738 47306 239890 1308890 6664130

1730 7154 28170 127586 546362 2630882 11903466

8738 28170 87698 334938 1224482 5236698 21220178

47306 127586 334938 1108418 3530906 13445762 48741018

239890 546362 1224482 3530906 9883666 33745850 110368418

1308890 2630882 5236698 13445762 33745850 104373122 311077338

6664130 11903466 21220178 48741018 110368418 311077338 850224914

36647114 59901074 98011242 204403250 422926922 1093447730 2760580074

187332082 281693210 425712578 809806586 1539486130 3669275930 8598808130

1038190010 1465393634 2079662490 3649630466 6426536762 14155021442

Links

R. H. Hardin, Table of n, a(n) for n = 1..127

Formula

Empirical for column k (the k=3..4 recurrence works also for k=1..2; apparently all rows and columns satisfy the same order 36 recurrence):

k=1: [linear recurrence of order 7].

k=2: [order 31].

k=3: [order 36].

k=4: [same order 36].

Example

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

Crossrefs

Sequence in context: A114358 A158305 A237406 * A234705 A324629 A234704

Adjacent sequences: A234709 A234710 A234711 * A234713 A234714 A234715

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 29 2013

Status

approved