A230337 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally, vertically 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, 6, 0, 0, 34, 34, 0, 0, 218, 534, 218, 0, 0, 1386, 9162, 9162, 1386, 0, 0, 8810, 157200, 438284, 157200, 8810, 0, 0, 56010, 2696012, 20948996, 20948996, 2696012, 56010, 0, 0, 356074, 46237080, 1000237228, 2788320240, 1000237228, 46237080

Offset

1,5

Comments

Table starts

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

.0......6........34...........218.............1386.................8810

.0.....34.......534..........9162...........157200..............2696012

.0....218......9162........438284.........20948996...........1000237228

.0...1386....157200......20948996.......2788320240.........370609462746

.0...8810...2696012....1000237228.....370609462746......137077642883940

.0..56010..46237080...47762574418...49266883333526....50711260887195062

.0.356074.792976550.2280709396620.6549249195140490.18760268537988792192

Links

R. H. Hardin, Table of n, a(n) for n = 1..161

Formula

Empirical for column k:

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

k=2: a(n) = 5*a(n-1) +8*a(n-2) +4*a(n-3)

k=3: [order 9] for n>10

k=4: [order 24] for n>26

k=5: [order 64] for n>66

Example

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

Crossrefs

Sequence in context: A362791 A278014 A368846 * A019157 A019184 A019185

Adjacent sequences: A230334 A230335 A230336 * A230338 A230339 A230340

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 16 2013

Status

approved