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A268639 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once. 8
0, 3, 3, 12, 24, 12, 36, 120, 120, 36, 96, 504, 840, 504, 96, 240, 1944, 5178, 5178, 1944, 240, 576, 7128, 29772, 47640, 29772, 7128, 576, 1344, 25272, 163878, 412740, 412740, 163878, 25272, 1344, 3072, 87480, 875592, 3440052, 5419992, 3440052, 875592 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

....0......3........12..........36............96.............240

....3.....24.......120.........504..........1944............7128

...12....120.......840........5178.........29772..........163878

...36....504......5178.......47640........412740.........3440052

...96...1944.....29772......412740.......5419992........68710116

..240...7128....163878.....3440052......68710116......1328460312

..576..25272....875592....27906474.....849572724.....25093766490

.1344..87480...4578186...221913216...10310685036....465757993812

.3072.297432..23548164..1737860310..123340687488...8527096170390

.6912.997272.119570574.13445785116.1458578214948.154406753980596

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..420

FORMULA

Empirical for column k:

k=1: a(n) = 4*a(n-1) -4*a(n-2)

k=2: a(n) = 6*a(n-1) -9*a(n-2) for n>3

k=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4)

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

k=5: [order 10]

k=6: [order 14] for n>15

k=7: [order 26]

EXAMPLE

Some solutions for n=4 k=4

..2..0..0..0. .2..2..1..0. .0..0..0..0. .2..1..2..2. .0..1..2..2

..2..1..0..1. .2..1..0..0. .1..1..0..1. .2..2..1..0. .1..2..1..2

..1..0..1..2. .2..0..1..0. .2..2..1..2. .2..1..0..1. .2..1..0..2

..2..1..2..2. .2..1..0..1. .2..1..0..1. .1..2..1..2. .1..0..0..1

CROSSREFS

Column 1 is A167667(n-1).

Sequence in context: A052533 A268798 A136533 * A192307 A328150 A161804

Adjacent sequences:  A268636 A268637 A268638 * A268640 A268641 A268642

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 09 2016

STATUS

approved

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Last modified July 23 22:20 EDT 2021. Contains 346265 sequences. (Running on oeis4.)