A234882 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 1, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

32, 68, 68, 128, 148, 128, 268, 268, 268, 268, 512, 628, 472, 628, 512, 1068, 1188, 1116, 1116, 1188, 1068, 2048, 2944, 2096, 3336, 2096, 2944, 2048, 4268, 5684, 5316, 6364, 6364, 5316, 5684, 4268, 8192, 14604, 10240, 22748, 12208, 22748, 10240, 14604, 8192

Offset

1,1

Comments

Table starts

32 68 128 268 512 1068 2048 4268 8192

68 148 268 628 1188 2944 5684 14604 28492

128 268 472 1116 2096 5316 10240 27060 52744

268 628 1116 3336 6364 22748 44540 178572 353428

512 1188 2096 6364 12208 44348 87312 354132 703104

1068 2944 5316 22748 44348 261384 518988 3695496 7370908

2048 5684 10240 44540 87312 518988 1035792 7389460 14782992

4268 14604 27060 178572 354132 3695496 7389460 98517200 197023228

8192 28492 52744 353428 703104 7370908 14782992 197023228 394703128

17068 74816 142876 1512256 3038716 57766200 115949340 2946513328 5899223932

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Formula

Empirical for column k:

k=1: a(n) = 5*a(n-2) -4*a(n-4).

k=2: [order 9].

k=3: [order 11].

k=4: [order 19].

k=5: [order 23].

k=6: [order 31].

k=7: [order 35].

Example

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

Crossrefs

Sequence in context: A132773 A116349 A244341 * A043155 A039332 A043935

Adjacent sequences: A234879 A234880 A234881 * A234883 A234884 A234885

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 01 2014

Status

approved