A234443 T(n,k) is the number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 1 (constant-stress 1 X 1 tilings).

32, 120, 120, 448, 582, 448, 1680, 2804, 2804, 1680, 6272, 13676, 17200, 13676, 6272, 23520, 66228, 108404, 108404, 66228, 23520, 87808, 324556, 666880, 896112, 666880, 324556, 87808, 329280, 1578036, 4221580, 7165920, 7165920, 4221580, 1578036

Offset

1,1

Comments

Table starts

32 120 448 1680 6272 23520

120 582 2804 13676 66228 324556

448 2804 17200 108404 666880 4221580

1680 13676 108404 896112 7165920 59991972

6272 66228 666880 7165920 72539432 790261148

23520 324556 4221580 59991972 790261148 11533082488

87808 1578036 26023136 483370700 8028682984 153582428536

329280 7767916 165444308 4098064360 88710949848 2303823299344

1229312 37908724 1021780992 33256428216 904037477472 30988558369076

4609920 187373548 6523295060 285401797556 10133236760728 477592381790200

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

k=1: a(n) = 14*a(n-2).

k=2: a(n) = 5*a(n-1) +24*a(n-2) -130*a(n-3) +36*a(n-4) +80*a(n-5) -32*a(n-6).

k=3: [order 16].

k=4: [order 45].

Example

Some solutions for n=3, k=4:
  1 1 1 2 1      0 1 0 0 0      1 0 1 0 2      0 1 1 1 0
  2 1 0 2 0      2 2 2 1 0      0 0 0 0 1      1 1 2 1 1
  2 0 0 1 0      1 0 1 1 1      1 2 1 0 2      1 2 2 0 1
  2 1 0 2 0      2 2 2 1 2      0 2 0 0 1      2 2 1 0 0

Crossrefs

Sequence in context: A203721 A231527 A298201 * A234436 A297461 A297698

Adjacent sequences: A234440 A234441 A234442 * A234444 A234445 A234446

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 26 2013

Status

approved