A230675 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j)

0, 3, 0, 3, 15, 0, 9, 87, 81, 0, 15, 513, 1173, 423, 0, 33, 3387, 18915, 17271, 2247, 0, 63, 21933, 340563, 730503, 251595, 11925, 0, 129, 141411, 6081561, 37034355, 28368687, 3669765, 63291, 0, 255, 913245, 108108231, 1844154933, 4022141121, 1100265795

Offset

1,2

Comments

Table starts

.0......3.........3.............9...............15...................33

.0.....15........87...........513.............3387................21933

.0.....81......1173.........18915...........340563..............6081561

.0....423.....17271........730503.........37034355...........1844154933

.0...2247....251595......28368687.......4022141121.........559929294657

.0..11925...3669765....1100265795.....436827078531......169908632412447

.0..63291..53519163...42681522741...47444197636239....51564141085334199

.0.335943.780527655.1655698076319.5152946201086569.15648664251672721725

Links

R. H. Hardin, Table of n, a(n) for n = 1..126

Formula

Empirical for column k:

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

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

k=3: a(n) = 14*a(n-1) +9*a(n-2) -9*a(n-3) +30*a(n-4) -19*a(n-5)

k=4: [order 32]

k=5: [order 80]

Empirical for row n:

n=1: a(n) = a(n-1) +2*a(n-2)

n=2: a(n) = 5*a(n-1) +6*a(n-2) +20*a(n-3) +12*a(n-4) +8*a(n-5)

n=3: [order 15] for n>16

n=4: [order 64] for n>65

Example

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

Crossrefs

Column 2 is A229841

Row 1 is A062510(n-1)

Sequence in context: A211963 A275080 A128252 * A327673 A279657 A272722

Adjacent sequences: A230672 A230673 A230674 * A230676 A230677 A230678

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 27 2013

Status

approved