A234169 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 2 (constant-stress 1 X 1 tilings).

136, 766, 766, 4296, 4970, 4296, 24158, 32070, 32070, 24158, 135752, 208412, 236876, 208412, 135752, 764190, 1353986, 1773484, 1773484, 1353986, 764190, 4299592, 8846884, 13227132, 15427948, 13227132, 8846884, 4299592, 24233182, 57811490

Offset

1,1

Comments

Table starts

136 766 4296 24158 135752 764190

766 4970 32070 208412 1353986 8846884

4296 32070 236876 1773484 13227132 99877680

24158 208412 1773484 15427948 133660366 1183467658

135752 1353986 13227132 133660366 1337127500 13865878254

764190 8846884 99877680 1183467658 13865878254 171702282736

4299592 57811490 751361300 10438586426 142146253428 2098023535022

24233182 380032300 5729616704 94449496104 1522643238010 27538386579098

136504392 2498158614 43493374260 849993735464 16046511409532 353610525268640

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) +41*a(n-2) -132*a(n-3) -264*a(n-4).

k=2: [order 17].

k=3: [order 80].

Example

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

Crossrefs

Sequence in context: A076331 A183901 A270341 * A234162 A262091 A251175

Adjacent sequences: A234166 A234167 A234168 * A234170 A234171 A234172

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 20 2013

Status

approved