A234823 T(n,k) is the number of (n+1) X (k+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 6 (constant-stress 1 X 1 tilings).

168, 686, 686, 2380, 2220, 2380, 9716, 6282, 6282, 9716, 34092, 22098, 15224, 22098, 34092, 139112, 68570, 47136, 47136, 68570, 139112, 493348, 252486, 131704, 129384, 131704, 252486, 493348, 2011808, 828354, 443220, 325424, 325424, 443220, 828354

Offset

1,1

Comments

Table starts

168 686 2380 9716 34092 139112 493348 2011808

686 2220 6282 22098 68570 252486 828354 3136350

2380 6282 15224 47136 131704 443220 1352816 4791948

9716 22098 47136 129384 325424 994812 2794776 9151956

34092 68570 131704 325424 747192 2099300 5474032 16726940

139112 252486 443220 994812 2099300 5441232 13185612 37597992

493348 828354 1352816 2794776 5474032 13185612 29871848 79958916

2011808 3136350 4791948 9151956 16726940 37597992 79958916 201644928

7205628 10660586 15484360 27722816 47728392 100759412 202105408 481962668

29360336 41107950 56779452 95289828 154893260 307659576 583797684 1320262800

Links

R. H. Hardin, Table of n, a(n) for n = 1..197

Formula

Empirical for column k (the k=2..6 recurrence also works for column 1; apparently all rows and columns satisfy the same order 23 recurrence):

k=1: [linear recurrence of order 7].

k=2..6: [same recurrence of order 23].

Example

Some solutions for n=4, k=4:
  5 0 3 2 4      4 3 6 2 4      3 6 4 5 4      6 0 3 0 4
  2 3 0 5 1      1 6 3 5 1      5 2 6 1 6      3 3 0 3 1
  6 1 4 3 5      3 2 5 1 3      0 3 1 2 1      6 0 3 0 4
  2 3 0 5 1      1 6 3 5 1      4 1 5 0 5      3 3 0 3 1
  6 1 4 3 5      3 2 5 1 3      1 4 2 3 2      6 0 3 0 4

Crossrefs

Sequence in context: A234738 A234731 A157998 * A234816 A245868 A251461

Adjacent sequences: A234820 A234821 A234822 * A234824 A234825 A234826

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 31 2013

Status

approved