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A269152 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified July 17 16:58 EDT 2019. Contains 325107 sequences. (Running on oeis4.)