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A186579
T(n,k) = Number of (n+2) X (k+2) 0..4 arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.
2
1953125, 6266, 6266, 86439, 845, 86439, 214452, 2799, 2799, 214452, 572145, 23629, 23197, 23629, 572145, 1055951, 52923, 79371, 79371, 52923, 1055951, 1597074, 69181, 115469, 441869, 115469, 69181, 1597074, 1819733, 79441, 128929, 551969
OFFSET
1,1
COMMENTS
Table starts
.1953125...6266..86439..214452..572145.1055951.1597074..1819733..3690909
....6266....845...2799...23629...52923...69181...79441....91701...127401
...86439...2799..23197...79371..115469..128929..144389...179449...305149
..214452..23629..79371..441869..551969..583429..634489...759549..1071249
..572145..52923.115469..551969.1310469.1377529.1518589..1765649..2296949
.1055951..69181.128929..583429.1377529.1673469.1923729..2313589..3194089
.1597074..79441.144389..634489.1518589.1923729.2481269..3207529..4573229
.1819733..91701.179449..759549.1765649.2313589.3207529..4583469..6647169
.3690909.127401.305149.1071249.2296949.3194089.4573229..6647169.11621669
.6661577.262445.636689.2006389.4029289.5488429.7642369.11561509.19720409
LINKS
FORMULA
Empirical, for all columns: a(n) = 2*a(n-1)-a(n-2)+4*a(n-3)-8*a(n-4)+4*a(n-5)+4*a(n-6)-4*a(n-7) for n > 22,12,11,12,13,14,15,16 respectively for k=1..8.
EXAMPLE
Some solutions for 5 X 4
..0..0..3..1....0..0..0..4....0..3..0..2....0..4..4..0....0..0..1..1
..0..0..0..1....0..0..0..0....0..0..3..0....0..0..4..4....0..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..3....0..0..0..4....0..0..0..0
..0..0..0..0....1..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..3..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....1..4..0..0
CROSSREFS
Sequence in context: A251299 A220290 A186578 * A290500 A377162 A016821
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Feb 24 2011
STATUS
approved