A235198 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 5, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

136, 512, 512, 1880, 1544, 1880, 7072, 4724, 4724, 7072, 26040, 15604, 12176, 15604, 26040, 98080, 51144, 35868, 35868, 51144, 98080, 361688, 176104, 105208, 96848, 105208, 176104, 361688, 1364512, 597712, 333340, 261760, 261760, 333340, 597712

Offset

1,1

Comments

Table starts

136 512 1880 7072 26040 98080 361688 1364512

512 1544 4724 15604 51144 176104 597712 2109748

1880 4724 12176 35868 105208 333340 1043256 3446068

7072 15604 35868 96848 261760 774140 2263256 7020392

26040 51144 105208 261760 652872 1816160 4984584 14642048

98080 176104 333340 774140 1816160 4812096 12604104 35505020

361688 597712 1043256 2263256 4984584 12604104 31498952 85424552

1364512 2109748 3446068 7020392 14642048 35505020 85424552 224694240

5038200 7324940 11230320 21497244 42396520 98577596 227963432 582078148

19038496 26321996 38241780 68985912 129109408 287939516 642257224 1596252448

Links

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

Formula

Empirical for column k (the k=3..6 recurrence works also for k=1..2; apparently all rows and columns satisfy the same order 39 recurrence):

k=1: a(n) = 30*a(n-2) -257*a(n-4) +468*a(n-6).

k=2: [order 23].

k=3..6: [same order 39 recurrence].

Example

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

Crossrefs

Sequence in context: A183635 A116223 A124241 * A235191 A076331 A183901

Adjacent sequences: A235195 A235196 A235197 * A235199 A235200 A235201

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 04 2014

Status

approved