A269052 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

3, 9, 9, 24, 42, 27, 60, 102, 174, 81, 144, 360, 594, 666, 243, 336, 1068, 3078, 3258, 2430, 729, 768, 3288, 13140, 24192, 17346, 8586, 2187, 1728, 9864, 58752, 149358, 183072, 90450, 29646, 6561, 3840, 29472, 253416, 971844, 1643376, 1350672, 464250

Offset: 1

Author

R. H. Hardin, Feb 18 2016

Keywords

• nonn
• tabl

Comments

Table starts

.....3.......9.......24.........60..........144............336.............768

.....9......42......102........360.........1068...........3288............9864

....27.....174......594.......3078........13140..........58752..........253416

....81.....666.....3258......24192.......149358.........971844.........6053094

...243....2430....17346.....183072......1643376.......15547380.......140497512

...729....8586....90450....1350672.....17696520......242861616......3193266318

..2187...29646...464250....9779808....187575858.....3726221592.....71430596250

..6561..100602..2353338...69793968...1964080920....56376679620...1577976495486

.19683..336798.11809746..492374976..20365312416...843461153880..34509932303172

.59049.1115370.58773858.3441051984.209472681102.12504078167988.748499855355192

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..337

Crossrefs

Column 1 is A000244.

Column 2 is A268622.

Row 1 is A084858.

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1)

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) for n>5

k=4: a(n) = 14*a(n-1) -57*a(n-2) +56*a(n-3) -16*a(n-4) for n>5

k=5: [order 12] for n>13

k=6: [order 18] for n>19

k=7: [order 38] for n>39

Empirical for row n:

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

n=2: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4)

n=3: a(n) = 6*a(n-1) -a(n-2) -28*a(n-3) -4*a(n-4) +16*a(n-5) -4*a(n-6) for n>8

n=4: [order 12] for n>14

n=5: [order 20] for n>22

n=6: [order 46] for n>48

n=7: [order 92] for n>94