A300138 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 16, 2, 1, 1, 5, 17, 17, 5, 1, 1, 9, 88, 27, 88, 9, 1, 1, 22, 209, 204, 204, 209, 22, 1, 1, 45, 673, 667, 2156, 667, 673, 45, 1, 1, 101, 1898, 3273, 11439, 11439, 3273, 1898, 101, 1, 1, 218, 5663, 13765, 80126, 98708, 80126, 13765, 5663, 218

Offset

1,12

Comments

Table starts

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

.1...1....1.....2.......5.........9.........22...........45............101

.1...1...16....17......88.......209........673.........1898...........5663

.1...2...17....27.....204.......667.......3273........13765..........61625

.1...5...88...204....2156.....11439......80126.......539828........3690822

.1...9..209...667...11439.....98708....1118800.....12484789......140924631

.1..22..673..3273...80126...1118800...20405641....375468115.....6965745267

.1..45.1898.13765..539828..12484789..375468115..11565870189...357938887736

.1.101.5663.61625.3690822.140924631.6965745267.357938887736.18502726008627

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

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

k=3: [order 10] for n>12

k=4: [order 28] for n>29

Example

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

Crossrefs

Column 2 is A052962(n-2).

Sequence in context: A155955 A221076 A230513 * A362884 A217028 A145684

Adjacent sequences: A300135 A300136 A300137 * A300139 A300140 A300141

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 26 2018

Status

approved