A234227 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 3 (constant-stress 1 X 1 tilings).

104, 436, 436, 1824, 1560, 1824, 7696, 5612, 5612, 7696, 32384, 20724, 17448, 20724, 32384, 137536, 76972, 56936, 56936, 76972, 137536, 582144, 293316, 188040, 167688, 188040, 293316, 582144, 2488576, 1123724, 648536, 503272, 503272, 648536

Offset

1,1

Comments

Table starts

104 436 1824 7696 32384 137536 582144

436 1560 5612 20724 76972 293316 1123724

1824 5612 17448 56936 188040 648536 2264904

7696 20724 56936 167688 503272 1597896 5162984

32384 76972 188040 503272 1379816 4055128 12178344

137536 293316 648536 1597896 4055128 11145960 31418264

582144 1123724 2264904 5162984 12178344 31418264 83324136

2488576 4410276 8215256 17479656 38671960 94267656 236748824

10594304 17381356 30142344 60126376 125308904 289507096 690049704

45577216 70026180 114224792 215032104 425135512 935746056 2128516184

Links

R. H. Hardin, Table of n, a(n) for n = 1..179

Formula

Empirical for column k (the k=4 recurrence also works for k=1..3; apparently the same order 16 recurrence works for all rows and columns):

k=1: a(n) = 4*a(n-1) +20*a(n-2) -80*a(n-3).

k=2: a(n) = 7*a(n-1) +20*a(n-2) -224*a(n-3) +144*a(n-4) +1680*a(n-5) -2880*a(n-6).

k=3: [order 11].

k=4: [order 16].

k=5: [same order 16].

k=6: [same order 16].

k=7: [same order 16].

Example

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

Crossrefs

Sequence in context: A220063 A135441 A188150 * A234220 A234208 A234201

Adjacent sequences: A234224 A234225 A234226 * A234228 A234229 A234230

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 21 2013

Status

approved