A231031 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 at least one element with value (x(i,j)-1) mod 3, and upper left element zero

0, 0, 0, 0, 2, 0, 0, 12, 12, 0, 0, 62, 60, 62, 0, 0, 344, 1074, 1074, 344, 0, 0, 1864, 12400, 43566, 12400, 1864, 0, 0, 10162, 162288, 1444702, 1444702, 162288, 10162, 0, 0, 55324, 2049324, 50554618, 124446770, 50554618, 2049324, 55324, 0, 0, 301278

Offset

1,5

Comments

Table starts

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

.0.....2.......12..........62............344...............1864

.0....12.......60........1074..........12400.............162288

.0....62.....1074.......43566........1444702...........50554618

.0...344....12400.....1444702......124446770........11542542126

.0..1864...162288....50554618....11542542126......2846678305070

.0.10162..2049324..1740086452..1050541512334....688099769580280

.0.55324.26149710.60169326764.96084401660280.167200150832484832

Links

R. H. Hardin, Table of n, a(n) for n = 1..127

Formula

Empirical for column k:

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

k=3: [order 28]

Example

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

Crossrefs

Sequence in context: A350909 A244139 A350732 * A061848 A193294 A231049

Adjacent sequences: A231028 A231029 A231030 * A231032 A231033 A231034

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 03 2013

Status

approved