A235289 T(n,k) is the number of (n+1) X (k+1) 0..3 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4 (constant-stress 1 X 1 tilings).

20, 40, 40, 68, 68, 68, 136, 104, 104, 136, 236, 188, 148, 188, 236, 472, 304, 248, 248, 304, 472, 836, 572, 380, 380, 380, 572, 836, 1672, 968, 680, 544, 544, 680, 968, 1672, 3020, 1868, 1108, 908, 740, 908, 1108, 1868, 3020, 6040, 3280, 2072, 1400, 1168, 1168

Offset

1,1

Comments

Table starts

20 40 68 136 236 472 836 1672 3020 6040 11108 22216 41516

40 68 104 188 304 572 968 1868 3280 6428 11624 22988 42544

68 104 148 248 380 680 1108 2072 3548 6824 12148 23768 43580

136 188 248 380 544 908 1400 2492 4096 7628 13208 25340 45664

236 304 380 544 740 1168 1724 2944 4676 8464 14300 26944 47780

472 572 680 908 1168 1724 2408 3884 5872 10172 16520 30188 52048

836 968 1108 1400 1724 2408 3220 4952 7196 12008 18868 33560 56444

1672 1868 2072 2492 2944 3884 4952 7196 9952 15788 23672 40412 65344

3020 3280 3548 4096 4676 5872 7196 9952 13220 20080 28988 47776 74756

6040 6428 6824 7628 8464 10172 12008 15788 20080 28988 39944 62828 93904

Empirical: T(n,k) is the number of (n+1) X (k+1) 0..2+i arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 2+2*i (constant-stress 1 X 1 tilings) for i=1..4(..?).

Links

R. H. Hardin, Table of n, a(n) for n = 1..568

Formula

Empirical for column k (the recurrence for k=2..7 also works for k=1; apparently every row and column satisfies the same order 6 recurrence):

diagonal: a(n) = a(n-1) +9*a(n-2) -9*a(n-3) -26*a(n-4) +26*a(n-5) +24*a(n-6) -24*a(n-7).

k=1: a(n) = 2*a(n-1) +3*a(n-2) -6*a(n-3).

k=2..7: a(n) = 3*a(n-1) +3*a(n-2) -15*a(n-3) +4*a(n-4) +18*a(n-5) -12*a(n-6).

Example

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

Crossrefs

Sequence in context: A333234 A040380 A154044 * A296764 A046794 A104153

Adjacent sequences: A235286 A235287 A235288 * A235290 A235291 A235292

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 05 2014

Status

approved