A234658 T(n,k) is the number of (n+1) X (k+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4 (constant-stress 1 X 1 tilings).

160, 728, 728, 3264, 2648, 3264, 15008, 9616, 9616, 15008, 67840, 37352, 28496, 37352, 67840, 315008, 144512, 94432, 94432, 144512, 315008, 1434624, 593048, 315024, 274520, 315024, 593048, 1434624, 6722048, 2414992, 1148176, 808160

Offset

1,1

Comments

Table starts

160 728 3264 15008 67840 315008 1434624

728 2648 9616 37352 144512 593048 2414992

3264 9616 28496 94432 315024 1148176 4196144

15008 37352 94432 274520 808160 2646344 8731840

67840 144512 315024 808160 2113072 6250544 18735792

315008 593048 1148176 2646344 6250544 16899896 46510768

1434624 2414992 4196144 8731840 18735792 46510768 118121744

6722048 10359416 16491760 31384136 61854032 142026104 335161744

30822400 43905728 64635984 113059808 205847920 438922928 966751344

145614848 194994488 269420656 437774312 742330832 1476803288 3047922832

Links

R. H. Hardin, Table of n, a(n) for n = 1..178

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) +44*a(n-2) -176*a(n-3) -480*a(n-4) +1920*a(n-5).

k=2: [order 15].

k=3: [order 21].

k=4: [order 23].

Example

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

Crossrefs

Sequence in context: A278122 A233917 A233910 * A234651 A234898 A234891

Adjacent sequences: A234655 A234656 A234657 * A234659 A234660 A234661

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 29 2013

Status

approved