A204284 T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..2 introduced in row major order

108, 274, 274, 783, 622, 783, 1758, 865, 865, 1758, 5263, 193, 128, 193, 5263, 14141, 539, 256, 256, 539, 14141, 29731, 735, 334, 244, 334, 735, 29731, 93809, 1883, 778, 442, 442, 778, 1883, 93809, 248919, 5187, 1990, 982, 736, 982, 1990, 5187, 248919

Offset

1,1

Comments

Table starts

...108..274..783.1758.5263.14141.29731.93809.248919.573623.1749927.4584571

...274..622..865..193..539...735..1883..5187..12715..34507...94379..254955

...783..865..128..256..334...778..1990..4758..12782..34702...93502..255070

..1758..193..256..244..442...982..1914..4922..13138..34498...93778..255730

..5263..539..334..442..736...996..2168..5368..13024..34864...94528..255360

.14141..735..778..982..996..1496..2860..5500..13636..35860...94404..256196

.29731.1883.1990.1914.2168..2860..3664..6784..15304..36408...95912..258472

.93809.5187.4758.4922.5368..5500..6784.10288..17688..39752..100024..260344

Links

R. H. Hardin, Table of n, a(n) for n = 1..337

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -3*a(n-2) +10*a(n-3) -44*a(n-4) +60*a(n-5) -30*a(n-6) -172*a(n-7) -152*a(n-8) +1224*a(n-9) -448*a(n-10) -656*a(n-11) +880*a(n-12) -2592*a(n-13) +2688*a(n-14) -768*a(n-15) for n>16

k=2: a(n) = 3*a(n-1) -6*a(n-4) +4*a(n-6) for n>9

k=3..7: a(n) = 3*a(n-1) -6*a(n-4) +4*a(n-6) for n>8

Example

Some solutions for n=4 k=3
..0..0..0..0..0....0..0..0..0..0....0..0..0..1..2....0..0..0..0..0
..0..0..0..0..0....1..1..1..1..1....2..0..0..0..1....0..0..0..0..0
..1..1..1..1..1....0..0..0..0..0....2..2..0..0..0....1..1..1..1..1
..0..0..0..0..0....0..0..0..0..0....2..2..2..0..0....0..0..0..0..0
..2..2..2..2..2....1..1..1..1..1....0..2..2..2..0....1..1..1..1..1
..2..2..2..2..2....0..0..0..0..0....0..1..2..2..2....2..2..2..2..2

Crossrefs

Sequence in context: A255091 A255084 A252337 * A204277 A138669 A304377

Adjacent sequences: A204281 A204282 A204283 * A204285 A204286 A204287

Keyword

nonn,tabl

Author

R. H. Hardin Jan 13 2012

Status

approved