A268774 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

0, 3, 3, 12, 12, 12, 36, 32, 32, 36, 96, 100, 112, 100, 96, 240, 248, 446, 446, 248, 240, 576, 620, 1524, 2296, 1524, 620, 576, 1344, 1456, 5214, 10340, 10340, 5214, 1456, 1344, 3072, 3380, 17000, 46312, 64112, 46312, 17000, 3380, 3072, 6912, 7656, 54822

Offset

1,2

Comments

Table starts

....0.....3.....12.......36........96.........240..........576..........1344

....3....12.....32......100.......248.........620.........1456..........3380

...12....32....112......446......1524........5214........17000.........54822

...36...100....446.....2296.....10340.......46312.......198114........837848

...96...248...1524....10340.....64112......387146......2258084......12951796

..240...620...5214....46312....387146.....3104544.....24222418.....185142872

..576..1456..17000...198114...2258084....24222418....255353744....2624246370

.1344..3380..54822...837848..12951796...185142872...2624246370...36091542548

.3072..7656.173244..3472210..73011192..1393319226..26623649020..491176316484

.6912.17148.541910.14245712.406925194.10357051740.266457432340.6585970939900

Links

R. H. Hardin, Table of n, a(n) for n = 1..612

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -4*a(n-4) for n>5

k=3: a(n) = 4*a(n-1) +2*a(n-2) -16*a(n-3) -a(n-4) +12*a(n-5) -4*a(n-6) for n>8

k=4: [order 8] for n>10

k=5: [order 12] for n>14

k=6: [order 16] for n>18

k=7: [order 28] for n>30

Example

Some solutions for n=4 k=4
..2..1..2..2. .1..2..2..2. .0..0..0..0. .0..1..0..1. .2..2..1..2
..1..2..2..1. .2..2..2..1. .1..0..1..0. .0..0..0..1. .2..2..2..2
..2..2..2..2. .2..1..2..2. .0..0..0..0. .0..0..0..0. .1..2..2..2
..2..1..2..1. .1..2..2..2. .1..1..0..1. .0..0..0..1. .2..1..2..2

Crossrefs

Column 1 is A167667(n-1).

Sequence in context: A153270 A065957 A303309 * A240801 A032308 A117856

Adjacent sequences: A268771 A268772 A268773 * A268775 A268776 A268777

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 13 2016

Status

approved