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).

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

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