A230526 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally, vertically, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero

0, 0, 0, 0, 12, 0, 0, 78, 78, 0, 0, 576, 1408, 576, 0, 0, 4374, 29618, 29618, 4374, 0, 0, 32832, 627350, 1787448, 627350, 32832, 0, 0, 246726, 13230788, 110423366, 110423366, 13230788, 246726, 0, 0, 1854576, 279167078, 6768331956, 19885757988

Offset

1,5

Comments

Table starts

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

.0......12.........78............576...............4374.................32832

.0......78.......1408..........29618.............627350..............13230788

.0.....576......29618........1787448..........110423366............6768331956

.0....4374.....627350......110423366........19885757988.........3550368078592

.0...32832...13230788.....6768331956......3550368078592......1844551938024312

.0..246726..279167078...415065958262....634283945584134....959021374133908722

.0.1854576.5890518102.25457364392092.113331393339170666.498682290491203324876

Links

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

Formula

Empirical for column k:

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

k=2: a(n) = 6*a(n-1) +9*a(n-2) +18*a(n-3)

k=3: [order 9]

k=4: [order 15]

k=5: [order 52]

Example

Some solutions for n=3 k=4
..0..2..0..2....0..2..2..2....0..2..1..2....0..0..0..2....0..1..0..0
..1..0..1..2....2..1..1..0....2..1..2..0....1..0..1..0....0..2..1..2
..2..1..2..0....0..2..1..2....0..0..1..1....2..0..2..1....2..1..1..1

Crossrefs

Sequence in context: A347802 A230926 A064141 * A156401 A246223 A199542

Adjacent sequences: A230523 A230524 A230525 * A230527 A230528 A230529

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 22 2013

Status

approved