A234921 T(n,k) is the number of (n+1) X (k+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 2, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

40, 120, 120, 376, 360, 376, 1200, 1128, 1128, 1200, 3848, 3912, 3684, 3912, 3848, 12360, 13368, 13336, 13336, 13368, 12360, 39720, 47980, 49056, 55492, 49056, 47980, 39720, 127664, 169128, 186500, 221272, 221272, 186500, 169128, 127664, 410344

Offset

1,1

Comments

Table starts

40 120 376 1200 3848 12360 39720

120 360 1128 3912 13368 47980 169128

376 1128 3684 13336 49056 186500 710304

1200 3912 13336 55492 221272 990956 4151672

3848 13368 49056 221272 991144 4834440 22970144

12360 47980 186500 990956 4834440 28854040 150606424

39720 169128 710304 4151672 22970144 150606424 911837036

127664 615344 2755840 19178920 115287720 948274980 6251426440

410344 2208840 10693364 82629808 562322520 5093099972 39266933948

1318968 8101636 42087616 389619632 2874164624 33282246680 276635826688

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -2*a(n-2) -2*a(n-3) +a(n-4).

k=2: [order 13].

k=3: [order 19].

k=4: [order 54].

Example

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

Crossrefs

Sequence in context: A235886 A261191 A260601 * A199807 A199810 A185762

Adjacent sequences: A234918 A234919 A234920 * A234922 A234923 A234924

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 01 2014

Status

approved