The On-Line Encyclopedia of Integer Sequences (OEIS)

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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.
(history; published version)

#6 by Alois P. Heinz at Tue Apr 19 18:34:25 EDT 2022

STATUS

editing

approved

#5 by Alois P. Heinz at Tue Apr 19 18:34:21 EDT 2022

NAME

T(n,k) = Number of nXk 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.

STATUS

approved

editing

#4 by R. H. Hardin at Sun Jun 09 08:42:30 EDT 2019

STATUS

editing

approved

#3 by R. H. Hardin at Sun Jun 09 08:42:27 EDT 2019

LINKS

R. H. Hardin, <a href="/A326165/b326165.txt">Table of n, a(n) for n = 1..199</a>

#2 by R. H. Hardin at Sun Jun 09 08:42:13 EDT 2019

NAME

allocated for R. H. Hardin

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.

DATA

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

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.

KEYWORD

allocated

nonn,tabl

AUTHOR

R. H. Hardin, Jun 09 2019

STATUS

approved

editing

#1 by R. H. Hardin at Sun Jun 09 08:35:48 EDT 2019

NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved