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A234564 T(n,k) is the number of (n+1) X (k+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4 (constant-stress 1 X 1 tilings). 9
70, 220, 220, 618, 546, 618, 1954, 1240, 1240, 1954, 5506, 3384, 2390, 3384, 5506, 17518, 8416, 5710, 5710, 8416, 17518, 49506, 24420, 12750, 11982, 12750, 24420, 49506, 158518, 64240, 33946, 23830, 23830, 33946, 64240, 158518, 449170, 194124 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

       70     220     618    1954    5506   17518   49506   158518   449170

      220     546    1240    3384    8416   24420   64240   194124   527920

      618    1240    2390    5710   12750   33946   83438   238306   621918

     1954    3384    5710   11982   23830   57210  128614   339234   831334

     5506    8416   12750   23830   42982   94114  195558   479914  1108726

    17518   24420   33946   57210   94114  187686  358450   810702  1742578

    49506   64240   83438  128614  195558  358450  635654  1336954  2694006

   158518  194124  238306  339234  479914  810702 1336954  2614518  4927738

   449170  527920  621918  831334 1108726 1742578 2694006  4927738  8740870

  1447510 1640076 1862530 2348514 2964106 4339470 6297370 10773174 17998810

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..364

FORMULA

Empirical for column k: (column 2..7 recurrence works also for k=1; apparently all rows and columns satisfy the same order 14 recurrence):

k=1: a(n) = 3*a(n-1) +18*a(n-2) -54*a(n-3) -80*a(n-4) +240*a(n-5).

k=2..7: [same order 14 recurrence].

EXAMPLE

Some solutions for n=5, k=4:

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

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

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

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

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

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

CROSSREFS

Sequence in context: A153669 A235310 A235303 * A234557 A245857 A227879

Adjacent sequences:  A234561 A234562 A234563 * A234565 A234566 A234567

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 28 2013

STATUS

approved

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Last modified September 25 06:22 EDT 2022. Contains 356959 sequences. (Running on oeis4.)