A234890 T(n,k) is the number of (n+1) X (k+1) 0..5 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).

80, 272, 272, 856, 980, 856, 2896, 3164, 3164, 2896, 9192, 11984, 10640, 11984, 9192, 31064, 40856, 43680, 43680, 40856, 31064, 98696, 159004, 163352, 209740, 163352, 159004, 98696, 333456, 551048, 706992, 884976, 884976, 706992, 551048, 333456

Offset

1,1

Comments

Table starts

80 272 856 2896 9192 31064 98696

272 980 3164 11984 40856 159004 551048

856 3164 10640 43680 163352 706992 2734000

2896 11984 43680 209740 884976 4616452 20512760

9192 40856 163352 884976 4318800 26272908 138216800

31064 159004 706992 4616452 26272908 198069616 1249781316

98696 551048 2734000 20512760 138216800 1249781316 9589218960

333456 2185372 12203144 112743844 902409352 10302188956 97684673000

1059616 7639428 47902816 512846088 4907082840 68182126892 792839750040

3579832 30731272 218388912 2929812696 33616093680 598458783660 8760287132596

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

Empirical for column k:

k=1: a(n) = 14*a(n-2) -37*a(n-4) +21*a(n-6).

k=2: [order 27].

k=3: [order 46].

Example

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

Crossrefs

Sequence in context: A235098 A235091 A306434 * A157912 A234883 A194646

Adjacent sequences: A234887 A234888 A234889 * A234891 A234892 A234893

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 01 2014

Status

approved