A297814 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2 or 3 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 1, 0, 1, 0, 0, 8, 2, 2, 8, 0, 0, 5, 0, 8, 0, 5, 0, 0, 22, 2, 13, 13, 2, 22, 0, 0, 29, 0, 27, 24, 27, 0, 29, 0, 0, 60, 2, 41, 41, 41, 41, 2, 60, 0, 0, 121, 0, 100, 39, 83, 39, 100, 0, 121, 0, 0, 194, 2, 208, 109, 114, 114, 109, 208, 2, 194, 0, 0, 425, 0, 450, 216

Offset

1,8

Comments

Table starts

.0..0.0...0...0...0...0....0....0....0.....0.....0.....0......0......0......0

.0..1.2...1...8...5..22...29...60..121...194...425...704...1421...2574...4821

.0..2.0...2...0...2...0....2....0....2.....0.....2.....0......2......0......2

.0..1.2...8..13..27..41..100..208..450...898..1871..3889...8201..17095..35607

.0..8.0..13..24..41..39..109..216..471...883..1826..3771...7957..16180..33265

.0..5.2..27..41..83.114..275..686.1545..3209..6926.15327..34142..75795.168685

.0.22.0..41..39.114..88..296..499.1270..2439..5497.12108..26721..58621.128316

.0.29.2.100.109.275.296..838.1536.3386..6644.14894.31159..67658.141516.309122

.0.60.0.208.216.686.499.1536.2234.6236.10650.25616.49634.113261.233334.522754

Links

R. H. Hardin, Table of n, a(n) for n = 1..611

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-2)

k=4: [order 14] for n>21

k=5: [order 12] for n>21

k=6: [order 40] for n>49

k=7: [order 49] for n>59

Example

Some solutions for n=7 k=4
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..1
..0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..0..1. .0..1..0..1
..1..0..1..0. .1..0..0..1. .0..1..0..1. .1..0..1..0. .1..0..1..0
..1..0..1..0. .0..1..1..0. .0..1..0..1. .1..0..1..0. .1..0..1..0
..1..0..1..0. .1..0..0..1. .0..1..0..1. .1..0..1..0. .0..1..0..1
..1..0..1..0. .0..1..1..0. .1..0..1..0. .0..1..1..0. .0..1..0..1
..1..1..0..0. .0..0..0..0. .1..1..0..0. .0..0..0..0. .0..0..1..1

Crossrefs

Sequence in context: A006997 A141612 A316342 * A298177 A298146 A295520

Adjacent sequences: A297811 A297812 A297813 * A297815 A297816 A297817

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 06 2018

Status

approved