A235258 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, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

184, 744, 744, 2672, 2592, 2672, 10820, 8328, 8328, 10820, 39680, 30300, 24232, 30300, 39680, 161060, 102000, 80812, 80812, 102000, 161060, 600928, 382036, 251656, 247368, 251656, 382036, 600928, 2443916, 1330480, 878988, 717452, 717452

Offset

1,1

Comments

Table starts

184 744 2672 10820 39680 161060 600928

744 2592 8328 30300 102000 382036 1330480

2672 8328 24232 80812 251656 878988 2873128

10820 30300 80812 247368 717452 2337832 7200188

39680 102000 251656 717452 1951752 5990204 17480904

161060 382036 878988 2337832 5990204 17318888 47995084

600928 1330480 2873128 7200188 17480904 47995084 126993640

2443916 5080484 10362212 24526880 56590772 147612912 373324260

9247456 18163048 35132248 79038828 174061880 434010540 1053946488

37667316 70306060 129681452 278130808 586251132 1398866408 3264942732

Links

R. H. Hardin, Table of n, a(n) for n = 1..160

Formula

Empirical for column k (the k=4..5 recurrence also works for k=1..3; apparently all rows and columns satisfy the same order 58 recurrence):

k=1: a(n) = 43*a(n-2) -617*a(n-4) +3073*a(n-6) -1762*a(n-8) +264*a(n-10).

k=2: [order 40].

k=3: [order 57].

k=4..5: [same order 58 recurrence].

Example

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

Crossrefs

Sequence in context: A217301 A351278 A239457 * A235251 A233676 A234152

Adjacent sequences: A235255 A235256 A235257 * A235259 A235260 A235261

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 05 2014

Status

approved