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A235280 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 5 (constant-stress 1 X 1 tilings). 11
40, 100, 100, 208, 208, 208, 520, 380, 380, 520, 1120, 844, 632, 844, 1120, 2800, 1660, 1280, 1280, 1660, 2800, 6208, 3844, 2344, 2344, 2344, 3844, 6208, 15520, 8012, 5096, 3952, 3952, 5096, 8012, 15520, 35200, 19060, 10088, 7936, 6232, 7936, 10088, 19060 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

     40    100    208    520   1120   2800   6208  15520  35200   88000  203008

    100    208    380    844   1660   3844   8012  19060  41500  100468  225740

    208    380    632   1280   2344   5096  10088  23000  48328  113720  249512

    520    844   1280   2344   3952   7936  14672  31504  62800  141424  298640

   1120   1660   2344   3952   6232  11704  20440  41704  79480  172360  352024

   2800   3844   5096   7936  11704  20440  33464  64168 115480  238024  463736

   6208   8012  10088  14672  20440  33464  51800  93992 160888  317192  593048

  15520  19060  23000  31504  41704  64168  93992 160888 260680  487960  867560

  35200  41500  48328  62800  79480 115480 160888 260680 401560  716200 1215928

  88000 100468 113720 141424 172360 238024 317192 487960 716200 1215928 1966280

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

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..420

FORMULA

Empirical for column k (the k=2..9 recurrence also works for k=1; apparently all rows and columns satisfy the same order 9 recurrence):

diagonal: [linear recurrence of order 11, computed assuming that all rows and columns satisfy the same order 9 recurrence].

k=1: a(n) = 10*a(n-2) -24*a(n-4).

k=2..9: [same order 9 recurrence].

EXAMPLE

Some solutions for n=4, k=4:

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

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

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

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

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

CROSSREFS

Sequence in context: A211493 A185791 A092889 * A235271 A033832 A235017

Adjacent sequences:  A235277 A235278 A235279 * A235281 A235282 A235283

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 05 2014

STATUS

approved

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Last modified October 2 08:34 EDT 2022. Contains 357191 sequences. (Running on oeis4.)