A326165 T(n,k) = Number of n X k 0..1 arrays with every element unequal to 0, 1, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 3, 3, 5, 6, 6, 5, 8, 11, 9, 11, 8, 13, 22, 25, 25, 22, 13, 21, 46, 60, 85, 60, 46, 21, 34, 91, 160, 261, 261, 160, 91, 34, 55, 182, 396, 838, 1136, 838, 396, 182, 55, 89, 371, 996, 2644, 5555, 5555, 2644, 996, 371, 89, 144, 746, 2480, 8646, 27902, 39808, 27902

Offset

1,2

Comments

Table starts

..1...2....3.....5......8.......13........21..........34...........55

..2...3....6....11.....22.......46........91.........182..........371

..3...6....9....25.....60......160.......396.........996.........2480

..5..11...25....85....261......838......2644........8646........28076

..8..22...60...261...1136.....5555.....27902......142396.......715457

.13..46..160...838...5555....39808....307759.....2396312.....18554951

.21..91..396..2644..27902...307759...3984553....50108120....631752599

.34.182..996..8646.142396..2396312..50108120..1000921717..20284433349

.55.371.2480.28076.715457.18554951.631752599.20284433349.666253766253

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) +a(n-2)

k=2: a(n) = a(n-1) +4*a(n-3) +a(n-5) -a(n-6)

k=3: [order 28] for n>30

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A318031.

Sequence in context: A301541 A240519 A318037 * A078462 A239518 A293924

Adjacent sequences: A326162 A326163 A326164 * A326166 A326167 A326168

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 09 2019

Status

approved