A277945 T(n,k)=Number of nXk 0..2 arrays with every element plus 1 mod 3 equal to some element at offset (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

0, 0, 0, 0, 3, 0, 0, 14, 14, 0, 0, 74, 172, 74, 0, 0, 377, 2353, 2353, 377, 0, 0, 1932, 31011, 84970, 31011, 1932, 0, 0, 9888, 410047, 2967962, 2967962, 410047, 9888, 0, 0, 50619, 5417792, 103960169, 273135341, 103960169, 5417792, 50619, 0, 0, 259118, 71585918

Offset

1,5

Comments

Table starts

.0....0.......0..........0.............0................0..................0

.0....3......14.........74...........377.............1932...............9888

.0...14.....172.......2353.........31011...........410047............5417792

.0...74....2353......84970.......2967962........103960169.........3638916907

.0..377...31011....2967962.....273135341......25229090418......2328401610722

.0.1932..410047..103960169...25229090418....6148196379968...1496942405776739

.0.9888.5417792.3638916907.2328401610722.1496942405776739.961449638681471934

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

Empirical for column k:

k=2: a(n) = 4*a(n-1) +6*a(n-2) -a(n-3) -2*a(n-4)

k=3: [order 20] for n>21

k=4: [order 70] for n>73

Example

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

Crossrefs

Sequence in context: A321711 A277788 A208848 * A169777 A338464 A278208

Adjacent sequences: A277942 A277943 A277944 * A277946 A277947 A277948

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 05 2016

Status

approved