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

Author

R. H. Hardin, Feb 13 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A167667(n-1).

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