A234490 T(n,k) is the number of (n+1) X (k+1) 0..3 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 2 (constant-stress 1 X 1 tilings).

62, 242, 242, 944, 926, 944, 3686, 3540, 3540, 3686, 14402, 13554, 13260, 13554, 14402, 56312, 51950, 49784, 49784, 51950, 56312, 220334, 199340, 187196, 183422, 187196, 199340, 220334, 862706, 765738, 705072, 677138, 677138, 705072, 765738

Offset

1,1

Comments

Table starts

62 242 944 3686 14402 56312 220334

242 926 3540 13554 51950 199340 765738

944 3540 13260 49784 187196 705072 2659824

3686 13554 49784 183422 677138 2505400 9288710

14402 51950 187196 677138 2455350 8928348 32545706

56312 199340 705072 2505400 8928348 31925284 114484712

220334 765738 2659824 9288710 32545706 114484712 404043442

862706 2944686 10049936 34509914 118945534 411823840 1431125914

3380192 11336132 38030588 128461544 435728940 1485448976 5084793448

13252982 43687010 144134184 479146446 1600124066 5373690488 18127421166

Links

R. H. Hardin, Table of n, a(n) for n = 1..179

Formula

Empirical for column k:

k=1: a(n) = 7*a(n-1) -9*a(n-2) -12*a(n-3).

k=2: a(n) = 10*a(n-1) -28*a(n-2) +a(n-3) +54*a(n-4) +24*a(n-5).

k=3: [order 11].

k=4: [order 18].

k=5: [order 31].

Example

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

Crossrefs

Sequence in context: A100423 A230007 A318561 * A234483 A158067 A045220

Adjacent sequences: A234487 A234488 A234489 * A234491 A234492 A234493

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 26 2013

Status

approved