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A326165 T(n,k)=Number of nXk 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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified July 7 23:03 EDT 2020. Contains 335502 sequences. (Running on oeis4.)