A268639 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.

0, 3, 3, 12, 24, 12, 36, 120, 120, 36, 96, 504, 840, 504, 96, 240, 1944, 5178, 5178, 1944, 240, 576, 7128, 29772, 47640, 29772, 7128, 576, 1344, 25272, 163878, 412740, 412740, 163878, 25272, 1344, 3072, 87480, 875592, 3440052, 5419992, 3440052, 875592

Offset

1,2

Comments

Table starts

....0......3........12..........36............96.............240

....3.....24.......120.........504..........1944............7128

...12....120.......840........5178.........29772..........163878

...36....504......5178.......47640........412740.........3440052

...96...1944.....29772......412740.......5419992........68710116

..240...7128....163878.....3440052......68710116......1328460312

..576..25272....875592....27906474.....849572724.....25093766490

.1344..87480...4578186...221913216...10310685036....465757993812

.3072.297432..23548164..1737860310..123340687488...8527096170390

.6912.997272.119570574.13445785116.1458578214948.154406753980596

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..0..0..0. .2..2..1..0. .0..0..0..0. .2..1..2..2. .0..1..2..2
..2..1..0..1. .2..1..0..0. .1..1..0..1. .2..2..1..0. .1..2..1..2
..1..0..1..2. .2..0..1..0. .2..2..1..2. .2..1..0..1. .2..1..0..2
..2..1..2..2. .2..1..0..1. .2..1..0..1. .1..2..1..2. .1..0..0..1

Crossrefs

Column 1 is A167667(n-1).

Sequence in context: A052533 A268798 A136533 * A192307 A328150 A161804

Adjacent sequences: A268636 A268637 A268638 * A268640 A268641 A268642

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 09 2016

Status

approved