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A268628 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once. 8
3, 9, 9, 24, 42, 24, 60, 174, 174, 60, 144, 666, 1086, 666, 144, 336, 2430, 6300, 6300, 2430, 336, 768, 8586, 34890, 55452, 34890, 8586, 768, 1728, 29646, 187224, 467190, 467190, 187224, 29646, 1728, 3840, 100602, 982086, 3819654, 6000978, 3819654 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

....3.......9........24..........60...........144.............336

....9......42.......174.........666..........2430............8586

...24.....174......1086........6300.........34890..........187224

...60.....666......6300.......55452........467190.........3819654

..144....2430.....34890......467190.......6000978........74914554

..336....8586....187224.....3819654......74914554......1430057208

..768...29646....982086....30553014.....915847266.....26758514760

.1728..100602...5063964...240364746...11018667294....493042858032

.3840..336798..25764066..1866503592..130903914954...8974328440044

.8448.1115370.129678528.14342680944.1539375100362.161737670836314

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

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

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

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

CROSSREFS

Column 1 is A084858.

Sequence in context: A207228 A207015 A268809 * A269052 A268971 A267966

Adjacent sequences:  A268625 A268626 A268627 * A268629 A268630 A268631

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 09 2016

STATUS

approved

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Last modified January 17 23:51 EST 2022. Contains 350410 sequences. (Running on oeis4.)