The On-Line Encyclopedia of Integer Sequences (OEIS)

Revisions by R. H. Hardin (See also R. H. Hardin's wiki page
and changes approved by R. H. Hardin)

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

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)

#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

A326164

Number of nX7 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)

#4 by R. H. Hardin at Sun Jun 09 08:41:43 EDT 2019

STATUS

editing

approved

#3 by R. H. Hardin at Sun Jun 09 08:41:41 EDT 2019

LINKS

R. H. Hardin, <a href="/A326164/b326164.txt">Table of n, a(n) for n = 1..210</a>

#2 by R. H. Hardin at Sun Jun 09 08:41:27 EDT 2019

NAME

allocated for R. H. Hardin

Number of nX7 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

21, 91, 396, 2644, 27902, 307759, 3984553, 50108120, 631752599, 7873793259, 97914938383, 1217849040638, 15154502797138, 188732168188613, 2350844998230808, 29285586927132940, 364802626463161313

OFFSET

1,1

COMMENTS

Column 7 of A326165.

EXAMPLE

Some solutions for n=5

..0..1..0..1..0..1..0. .0..0..1..0..1..0..1. .0..0..1..1..0..1..1

..0..1..1..0..1..0..0. .0..0..1..1..0..1..1. .0..0..0..0..1..1..1

..1..0..0..1..1..0..0. .1..0..1..0..0..1..0. .0..0..1..0..0..1..0

..0..0..1..0..0..0..1. .1..1..0..1..1..0..1. .0..0..1..1..0..0..1

..0..0..0..0..0..0..0. .1..0..1..0..1..0..1. .1..0..1..1..1..0..1

CROSSREFS

Cf. A326165.

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin, Jun 09 2019

STATUS

approved

editing

A326163

Number of nX6 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)

#4 by R. H. Hardin at Sun Jun 09 08:41:03 EDT 2019

STATUS

editing

approved

#3 by R. H. Hardin at Sun Jun 09 08:41:00 EDT 2019

LINKS

R. H. Hardin, <a href="/A326163/b326163.txt">Table of n, a(n) for n = 1..210</a>

#2 by R. H. Hardin at Sun Jun 09 08:40:38 EDT 2019

NAME

allocated for R. H. Hardin

Number of nX6 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

13, 46, 160, 838, 5555, 39808, 307759, 2396312, 18554951, 144011286, 1114725151, 8648561245, 67114777306, 521304493710, 4049638171109, 31461571016553, 244413499965088, 1898683692048684, 14749279061897812, 114573556996895961

OFFSET

1,1

COMMENTS

Column 6 of A326165.

EXAMPLE

Some solutions for n=5

..0..0..0..1..0..0. .0..0..1..0..1..1. .0..0..0..0..1..1. .0..0..1..0..1..1

..0..0..0..1..1..0. .0..0..1..0..0..1. .0..0..0..0..0..1. .1..1..0..1..1..0

..0..0..1..0..1..1. .1..1..0..1..1..1. .1..0..0..0..1..1. .0..1..0..1..1..1

..1..1..0..1..0..0. .0..1..1..0..0..1. .1..1..0..0..1..0. .1..1..1..1..1..1

..0..1..0..1..0..0. .0..0..1..0..0..0. .1..1..1..0..1..0. .1..1..1..1..1..1

CROSSREFS

Cf. A326165.

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin, Jun 09 2019

STATUS

approved

editing

A326162

Number of nX5 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)

#4 by R. H. Hardin at Sun Jun 09 08:40:16 EDT 2019

STATUS

editing

approved