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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000244.

Column 2 is A268622.

Row 1 is A084858.

Sequence in context: A207015 A268809 A268628 * A268971 A267966 A263320

Adjacent sequences: A269049 A269050 A269051 * A269053 A269054 A269055

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 18 2016

Status

approved