A235107 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 4, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

154, 670, 670, 2900, 2498, 2900, 12578, 9328, 9328, 12578, 54530, 35354, 30312, 35354, 54530, 236496, 135254, 101464, 101464, 135254, 236496, 1025770, 523532, 345280, 304746, 345280, 523532, 1025770, 4449942, 2047890, 1201872, 937034

Offset

1,1

Comments

Table starts

154 670 2900 12578 54530 236496 1025770

670 2498 9328 35354 135254 523532 2047890

2900 9328 30312 101464 345280 1201872 4256548

12578 35354 101464 304746 937034 2978124 9680994

54530 135254 345280 937034 2613410 7614452 22754394

236496 523532 1201872 2978124 7614452 20552136 57035088

1025770 2047890 4256548 9680994 22754394 57035088 147069470

4449942 8097130 15381300 32349918 70442910 165182704 398750942

19307284 32339728 56526280 110399304 223243440 490588960 1109052788

83782730 130423938 211590104 385970050 729220586 1509762708 3214407394

Links

R. H. Hardin, Table of n, a(n) for n = 1..178

Formula

Empirical for column k:

k=1: a(n) = 7*a(n-1) -2*a(n-2) -47*a(n-3) +3*a(n-4) +84*a(n-5) +36*a(n-6).

k=2: [order 19].

k=3: [order 62].

Example

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

Crossrefs

Sequence in context: A256024 A239564 A250626 * A235100 A230804 A200552

Adjacent sequences: A235104 A235105 A235106 * A235108 A235109 A235110

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 03 2014

Status

approved