A269097 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

0, 4, 4, 24, 96, 24, 108, 1152, 1152, 108, 432, 11424, 31296, 11424, 432, 1620, 103488, 715320, 715320, 103488, 1620, 5832, 889056, 15024096, 37963968, 15024096, 889056, 5832, 20412, 7375872, 300056400, 1856325000, 1856325000, 300056400, 7375872

Offset: 1

Author

R. H. Hardin, Feb 19 2016

Keywords

• nonn
• tabl

Comments

Table starts

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

......4.........96...........1152..............11424.................103488

.....24.......1152..........31296.............715320...............15024096

....108......11424.........715320...........37963968.............1856325000

....432.....103488.......15024096.........1856325000...........211625837280

...1620.....889056......300056400........86415197088.........22984646281176

...5832....7375872.....5795398368......3892946216856.......2416707037884480

..20412...59698464...109294975080....171307237216320.....248267055360211392

..69984..474360768..2024660774592...7406621052177000...25062609875880382656

.236196.3715826016.36988673403168.315868041326151072.2495854741014485439624

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..264

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) = 14*a(n-1) -49*a(n-2) for n>3

k=3: a(n) = 36*a(n-1) -378*a(n-2) +972*a(n-3) -729*a(n-4) for n>5

k=4: [order 6] for n>7

k=5: [order 14] for n>15

k=6: [order 26] for n>27

k=7: [order 64] for n>65