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

1,2

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

Links

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

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

Example

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

Crossrefs

Column 1 is A120908.

Sequence in context: A269186 A058166 A092897 * A269097 A307552 A171633

Adjacent sequences: A269149 A269150 A269151 * A269153 A269154 A269155

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 20 2016

Status

approved