A269152 T(n,k) = Number of n X k 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

0, 4, 4, 24, 80, 24, 108, 768, 768, 108, 432, 6224, 13904, 6224, 432, 1620, 46464, 220968, 220968, 46464, 1620, 5832, 330192, 3277728, 7002040, 3277728, 330192, 5832, 20412, 2270592, 46576336, 208984848, 208984848, 46576336, 2270592, 20412

Offset: 1

Author

R. H. Hardin, Feb 20 2016

Keywords

• nonn
• tabl

Comments

Table starts

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

......4........80...........768.............6224...............46464

.....24.......768.........13904...........220968.............3277728

....108......6224........220968..........7002040...........208984848

....432.....46464.......3277728........208984848.........12637025328

...1620....330192......46576336.......6004186984........738478504448

...5832...2270592.....642676704.....167970539096......42119837369168

..20412..15251152....8680278136....4607603633440....2359047063894464

..69984.100647168..115349343264..124496158984840..130272136732736736

.236196.655139152.1513379596864.3323815506994632.7113223023541150960

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..220

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) = 12*a(n-1) -38*a(n-2) +12*a(n-3) -a(n-4) for n>5

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

k=4: [order 20] for n>22

k=5: [order 42] for n>45