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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). 9
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified August 10 04:27 EDT 2022. Contains 356029 sequences. (Running on oeis4.)