A299135 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 13, 13, 1, 1, 42, 30, 42, 1, 1, 127, 149, 149, 127, 1, 1, 389, 576, 1261, 576, 389, 1, 1, 1192, 2621, 9316, 9316, 2621, 1192, 1, 1, 3645, 12495, 75592, 130924, 75592, 12495, 3645, 1, 1, 11161, 59426, 648807, 1969223, 1969223, 648807, 59426

Offset

1,5

Comments

Table starts

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

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

.1....13.....30......149........576..........2621...........12495

.1....42....149.....1261.......9316.........75592..........648807

.1...127....576.....9316.....130924.......1969223........31421743

.1...389...2621....75592....1969223......54173918......1576974771

.1..1192..12495...648807...31421743....1576974771.....83518793627

.1..3645..59426..5568411..497341456...45531416012...4394242516518

.1.11161.291819.48528385.7976508449.1330533860979.233738399148294

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 12] for n>14

k=4: [order 49] for n>51

Example

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

Crossrefs

Column 2 is A298234.

Sequence in context: A157177 A298240 A299366 * A299893 A299060 A299821

Adjacent sequences: A299132 A299133 A299134 * A299136 A299137 A299138

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 03 2018

Status

approved