A299821 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 13, 13, 1, 1, 42, 39, 42, 1, 1, 127, 202, 202, 127, 1, 1, 389, 894, 2101, 894, 389, 1, 1, 1192, 4507, 18101, 18101, 4507, 1192, 1, 1, 3645, 22684, 176353, 302780, 176353, 22684, 3645, 1, 1, 11161, 116651, 1735393, 5678641, 5678641

Offset

1,5

Comments

Table starts

.1.....1......1.........1...........1.............1................1

.1.....5.....13........42.........127...........389.............1192

.1....13.....39.......202.........894..........4507............22684

.1....42....202......2101.......18101........176353..........1735393

.1...127....894.....18101......302780.......5678641........107544794

.1...389...4507....176353.....5678641.....203062719.......7338573888

.1..1192..22684...1735393...107544794....7338573888.....506116118801

.1..3645.116651..17279857..2047783162..266405977942...35028322225854

.1.11161.605727.173340585.39237426288.9728685869763.2438361076801151

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 14] for n>16

k=4: [order 38] for n>39

Example

Some solutions for n=5 k=4
..0..1..1..1. .0..0..1..1. .0..0..1..1. .0..0..0..0. .0..0..0..1
..1..1..1..1. .0..1..1..1. .0..0..1..0. .0..0..0..0. .0..0..1..1
..0..1..1..1. .0..0..0..0. .0..1..1..1. .0..0..0..0. .1..0..0..0
..1..1..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..0. .0..0..0..0
..1..0..0..1. .0..0..0..0. .0..1..1..1. .1..0..1..1. .1..0..0..0

Crossrefs

Column 2 is A298234.

Sequence in context: A299135 A299893 A299060 * A299721 A300342 A119725

Adjacent sequences: A299818 A299819 A299820 * A299822 A299823 A299824

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 19 2018

Status

approved