A234564 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 4 (constant-stress 1 X 1 tilings).

70, 220, 220, 618, 546, 618, 1954, 1240, 1240, 1954, 5506, 3384, 2390, 3384, 5506, 17518, 8416, 5710, 5710, 8416, 17518, 49506, 24420, 12750, 11982, 12750, 24420, 49506, 158518, 64240, 33946, 23830, 23830, 33946, 64240, 158518, 449170, 194124

Offset

1,1

Comments

Table starts

70 220 618 1954 5506 17518 49506 158518 449170

220 546 1240 3384 8416 24420 64240 194124 527920

618 1240 2390 5710 12750 33946 83438 238306 621918

1954 3384 5710 11982 23830 57210 128614 339234 831334

5506 8416 12750 23830 42982 94114 195558 479914 1108726

17518 24420 33946 57210 94114 187686 358450 810702 1742578

49506 64240 83438 128614 195558 358450 635654 1336954 2694006

158518 194124 238306 339234 479914 810702 1336954 2614518 4927738

449170 527920 621918 831334 1108726 1742578 2694006 4927738 8740870

1447510 1640076 1862530 2348514 2964106 4339470 6297370 10773174 17998810

Links

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

Formula

Empirical for column k: (column 2..7 recurrence works also for k=1; apparently all rows and columns satisfy the same order 14 recurrence):

k=1: a(n) = 3*a(n-1) +18*a(n-2) -54*a(n-3) -80*a(n-4) +240*a(n-5).

k=2..7: [same order 14 recurrence].

Example

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

Crossrefs

Sequence in context: A153669 A235310 A235303 * A234557 A245857 A227879

Adjacent sequences: A234561 A234562 A234563 * A234565 A234566 A234567

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 28 2013

Status

approved