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A235319 T(n,k) is the number of (n+1) X (k+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 7 (constant-stress 1 X 1 tilings). 9
112, 392, 392, 1120, 1120, 1120, 3920, 2744, 2744, 3920, 11776, 8392, 5968, 8392, 11776, 41216, 22568, 16352, 16352, 22568, 41216, 128128, 71896, 40144, 40144, 40144, 71896, 128128, 448448, 206360, 118160, 89600, 89600, 118160, 206360 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

      112     392    1120     3920    11776    41216   128128    448448

      392    1120    2744     8392    22568    71896   206360    675064

     1120    2744    5968    16352    40144   118160   316912    978320

     3920    8392   16352    40144    89600   241600   598976   1723456

    11776   22568   40144    89600   184144   459536  1062832   2873552

    41216   71896  118160   241600   459536  1062832  2291696   5805424

   128128  206360  316912   598976  1062832  2291696  4632208  11046512

   448448  675064  978320  1723456  2873552  5805424 11046512  24862768

  1426432 2026472 2793040  4616960  7275856 13828496 24862768  52954448

  4992512 6751000 8912144 13917952 20859728 37480816 63985520 129456304

Empirical: T(n,k) is the number of (n+1) X (k+1) 0..5+i arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 5+2*i (constant-stress 1 X 1 tilings), for i=1..3(..?).

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..260

FORMULA

Empirical for column k (the k=2..6 recurrence also works for k=1; apparently all rows and columns satisfy the same order 18 recurrence):

k=1: a(n) = 28*a(n-2) - 252*a(n-4) + 720*a(n-6).

k=2..6: [same order 18 recurrence]

EXAMPLE

Some solutions for n=4, k=4:

  5 4 6 1 5    2 4 2 4 2    1 6 2 4 2    3 0 3 0 3

  0 6 1 3 0    6 1 6 1 6    4 2 5 0 5    1 5 1 5 1

  4 3 5 0 4    3 5 3 5 3    0 5 1 3 1    5 2 5 2 5

  0 6 1 3 0    5 0 5 0 5    4 2 5 0 5    2 6 2 6 2

  4 3 5 0 4    2 4 2 4 2    1 6 2 4 2    3 0 3 0 3

CROSSREFS

Sequence in context: A352585 A233892 A233885 * A203923 A235312 A203916

Adjacent sequences:  A235316 A235317 A235318 * A235320 A235321 A235322

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 05 2014

STATUS

approved

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Last modified August 11 20:13 EDT 2022. Contains 356067 sequences. (Running on oeis4.)