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A269097 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once. 8
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

LINKS

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

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

EXAMPLE

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

CROSSREFS

Column 1 is A120908.

Sequence in context: A058166 A092897 A269152 * A307552 A171633 A221276

Adjacent sequences:  A269094 A269095 A269096 * A269098 A269099 A269100

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 19 2016

STATUS

approved

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Last modified December 2 10:39 EST 2020. Contains 338876 sequences. (Running on oeis4.)