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.

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

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