A269186 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

0, 4, 4, 24, 48, 24, 108, 384, 384, 108, 432, 2736, 5888, 2736, 432, 1620, 18336, 80112, 80112, 18336, 1620, 5832, 118032, 1031344, 2097552, 1031344, 118032, 5832, 20412, 739008, 12791896, 52394312, 52394312, 12791896, 739008, 20412, 69984, 4533744

Offset

1,2

Comments

Table starts

......0.........4...........24.............108................432

......4........48..........384............2736..............18336

.....24.......384.........5888...........80112............1031344

....108......2736........80112.........2097552...........52394312

....432.....18336......1031344........52394312.........2563440512

...1620....118032.....12791896......1265974992.......121792778352

...5832....739008....154606864.....29881402560......5665397992608

..20412...4533744...1833130768....693021071760....259306140235672

..69984..27384288..21416076480..15854541802056..11718368891185840

.236196.163381968.247279304248.358760880894864.524154208020159720

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

Formula

Empirical for column k:

k=1: a(n) = 6*a(n-1) -9*a(n-2)

k=2: a(n) = 10*a(n-1) -21*a(n-2) -20*a(n-3) -4*a(n-4) for n>5

k=3: [order 8] for n>9

k=4: [order 16] for n>17

k=5: [order 40] for n>41

Example

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

Crossrefs

Column 1 is A120908.

Sequence in context: A088304 A131978 A049614 * A058166 A092897 A269152

Adjacent sequences: A269183 A269184 A269185 * A269187 A269188 A269189

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 20 2016

Status

approved