A186462 T(n,k)=Number of (n+1)X(k+1) binary arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors

16, 21, 21, 42, 30, 42, 61, 51, 51, 61, 106, 88, 111, 88, 106, 151, 128, 162, 162, 128, 151, 245, 197, 270, 309, 270, 197, 245, 359, 292, 362, 449, 449, 362, 292, 359, 567, 457, 590, 673, 797, 673, 590, 457, 567, 840, 688, 846, 945, 1061, 1061, 945, 846, 688, 840, 1301

Offset

1,1

Comments

Table starts

..16...21...42...61..106..151...245...359...567...840..1301...1941...2977

..21...30...51...88..128..197...292...457...688..1058..1589...2424...3651

..42...51..111..162..270..362...590...846..1362..1998..3122...4622...7126

..61...88..162..309..449..673...945..1493..2201..3473..5177...7993..11949

.106..128..270..449..797.1061..1681..2285..3681..5281..8437..12401..19317

.151..197..362..673.1061.1693..2377..3677..5073..7977.11533..18221..26957

.245..292..590..945.1681.2377..4121..5633..8893.11977.19037..27133..43249

.359..457..846.1493.2285.3677..5633..9477.13245.20281.27573..43177..62025

.567..688.1362.2201.3681.5073..8893.13245.22933.31217.48241..64785.102213

.840.1058.1998.3473.5281.7977.11977.20281.31217.52197.71885.109497.148069

Links

R. H. Hardin, Table of n, a(n) for n = 1..2449

Formula

Empirical, for every column: a(n)=2*a(n-1)-2*a(n-3)+2*a(n-4)-a(n-5) for n>max(8,k+6)

Example

Some solutions for 4X3
..1..0..0....1..1..0....1..0..1....1..0..1....0..1..0....1..0..1....0..0..0
..1..0..0....0..0..1....0..1..0....0..1..0....0..0..1....0..1..0....0..0..0
..0..1..0....0..0..0....1..0..1....1..0..1....0..0..0....0..0..1....0..0..0
..0..0..1....1..0..0....0..1..0....0..1..1....1..0..0....0..0..0....0..0..1

Crossrefs

Sequence in context: A167305 A094329 A070573 * A205098 A290142 A165160

Adjacent sequences: A186459 A186460 A186461 * A186463 A186464 A186465

Keyword

nonn,tabl

Author

R. H. Hardin Feb 22 2011

Status

approved