A234738 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 8 (constant-stress 1 X 1 tilings).

168, 672, 672, 2184, 2184, 2184, 8736, 6048, 6048, 8736, 29976, 21048, 14760, 21048, 29976, 119904, 64320, 45792, 45792, 64320, 119904, 426120, 233016, 127032, 127032, 127032, 233016, 426120, 1704480, 760608, 423072, 319488, 319488, 423072, 760608

Offset

1,1

Comments

Table starts

168 672 2184 8736 29976 119904 426120 1704480

672 2184 6048 21048 64320 233016 760608 2827992

2184 6048 14760 45792 127032 423072 1283880 4481376

8736 21048 45792 127032 319488 972888 2723040 8836536

29976 64320 127032 319488 737160 2072256 5395128 16400256

119904 233016 423072 972888 2072256 5395128 13083552 37239960

426120 760608 1283880 2723040 5395128 13083552 29705640 79520352

1704480 2827992 4481376 8836536 16400256 37239960 79520352 200901240

6197208 9650112 14469624 26699136 46685256 99668544 200901240 480387840

24788832 36532344 52195488 90688728 150256320 302942136 578901408 1314864792

Links

R. H. Hardin, Table of n, a(n) for n = 1..196

Formula

Empirical for column k (the k=2 recurrence also works for column 1; apparently every row and column satisfies the same order 23 recurrence):

k=1: a(n) = 4*a(n-1) +34*a(n-2) -136*a(n-3) -369*a(n-4) +1476*a(n-5) +1260*a(n-6) -5040*a(n-7).

k=2..6: [same order 23 recurrence].

Example

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

Crossrefs

Sequence in context: A027679 A137863 A266808 * A234731 A157998 A234823

Adjacent sequences: A234735 A234736 A234737 * A234739 A234740 A234741

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 30 2013

Status

approved