A235098 T(n,k) is the number of (n+1) X (k+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

80, 256, 256, 808, 656, 808, 2580, 1728, 1728, 2580, 8184, 4820, 3832, 4820, 8184, 26164, 13624, 9460, 9460, 13624, 26164, 83224, 39884, 23792, 21264, 23792, 39884, 83224, 266572, 117488, 63884, 48844, 48844, 63884, 117488, 266572, 849688, 354588

Offset

1,1

Comments

Table starts

80 256 808 2580 8184 26164 83224 266572 849688

256 656 1728 4820 13624 39884 117488 354588 1072888

808 1728 3832 9460 23792 63884 173440 491596 1403944

2580 4820 9460 21264 48844 121768 306532 813576 2175660

8184 13624 23792 48844 102336 238060 556560 1391140 3490704

26164 39884 63884 121768 238060 524728 1160340 2765568 6585764

83224 117488 173440 306532 556560 1160340 2420288 5516124 12489280

266572 354588 491596 813576 1391140 2765568 5516124 12147808 26512228

849688 1072888 1403944 2175660 3490704 6585764 12489280 26512228 55604120

2726852 3306172 4134548 6047320 9185772 16502816 29986228 61672784 125443708

Links

R. H. Hardin, Table of n, a(n) for n = 1..285

Formula

Empirical for column k (the k=4..7 recurrence works also for k=1..3; apparently every row and column satisfies the same order 23 recurrence):

k=1: a(n) = 3*a(n-1) +13*a(n-2) -39*a(n-3) -26*a(n-4) +78*a(n-5).

k=2: [order 16].

k=3: [order 22].

k=4..7: [same order 23].

Example

Some solutions for n=4, k=4:
  0 3 2 0 1      3 0 3 1 3      2 3 0 3 1      1 2 1 4 2
  1 0 3 5 2      1 2 1 3 1      4 1 2 1 3      4 1 4 3 5
  0 3 2 0 1      4 1 4 2 4      3 4 1 4 2      2 3 2 5 3
  1 0 3 5 2      1 2 1 3 1      4 1 2 1 3      4 1 4 3 5
  2 5 4 2 3      4 1 4 2 4      3 4 1 4 2      2 3 2 5 3

Crossrefs

Sequence in context: A202439 A203355 A203348 * A235091 A306434 A234890

Adjacent sequences: A235095 A235096 A235097 * A235099 A235100 A235101

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 03 2014

Status

approved