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

Author

R. H. Hardin, Feb 20 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A120908.

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