A230068 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j)

0, 0, 0, 0, 9, 0, 0, 9, 9, 0, 0, 81, 45, 81, 0, 0, 225, 441, 441, 225, 0, 0, 1089, 3645, 15129, 3645, 1089, 0, 0, 3969, 31329, 281961, 281961, 31329, 3969, 0, 0, 16641, 266805, 6487209, 14082255, 6487209, 266805, 16641, 0, 0, 65025, 2277081, 137945025

Offset

1,5

Comments

Table starts

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

.0.....9.......9.........81...........225.............1089................3969

.0.....9......45........441..........3645............31329..............266805

.0....81.....441......15129........281961..........6487209...........137945025

.0...225....3645.....281961......14082255........793041921.........43142680647

.0..1089...31329....6487209.....793041921.....114228452529......15615593045649

.0..3969..266805..137945025...43142680647...15615593045649....5392746297039195

.0.16641.2277081.3020271849.2369158188849.2168295406671681.1888668174848027049

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +6*a(n-2) -8*a(n-3)

k=3: a(n) = 7*a(n-1) +14*a(n-2) -8*a(n-3)

k=4: [order 10] for n>11

k=5: [order 16] for n>19

Example

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

Crossrefs

Column 2 is A208556(n-2)

Sequence in context: A132267 A021115 A073052 * A176908 A005083 A050453

Adjacent sequences: A230065 A230066 A230067 * A230069 A230070 A230071

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 08 2013

Status

approved