The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A208079 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A208079

Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 0 1 0 vertically.
(history; published version)

#10 by Alois P. Heinz at Sat Jan 20 12:40:38 EST 2018

STATUS

proposed

approved

#9 by Michel Marcus at Sat Jan 20 11:22:55 EST 2018

STATUS

editing

proposed

#8 by Michel Marcus at Sat Jan 20 11:22:49 EST 2018

AUTHOR

R. H. Hardin , Feb 23 2012

STATUS

proposed

editing

#7 by Colin Barker at Sat Jan 20 11:20:30 EST 2018

STATUS

editing

proposed

#6 by Colin Barker at Sat Jan 20 11:20:06 EST 2018

NAME

Number of 4Xn 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 0 1 0 vertically.

COMMENTS

Row 4 of A208078.

FORMULA

Empirical: a(n) = 5*a(n-1) + 5*a(n-2) - a(n-3).

Conjectures from Colin Barker, Jan 20 2018: (Start)

G.f.: 9*x*(1 + 4*x - x^2) / ((1 + x)*(1 - 6*x + x^2)).

a(n) = (9/4)*(2*(-1)^n + (3-2*sqrt(2))^n + (3+2*sqrt(2))^n).

(End)

EXAMPLE

Some solutions for n=4:

STATUS

approved

editing

#5 by Russ Cox at Sat Mar 31 12:37:21 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Feb 23 2012

Discussion

Sat Mar 31

12:37

OEIS Server: https://oeis.org/edit/global/875

#4 by Ron Hardin at Thu Feb 23 06:30:25 EST 2012

STATUS

editing

approved

#3 by Ron Hardin at Thu Feb 23 06:30:22 EST 2012

LINKS

R. H. Hardin, <a href="/A208079/b208079.txt">Table of n, a(n) for n = 1..210</a>

#2 by Ron Hardin at Thu Feb 23 06:30:00 EST 2012

NAME

allocated for Ron HardinNumber of 4Xn 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 0 1 0 vertically

DATA

9, 81, 441, 2601, 15129, 88209, 514089, 2996361, 17464041, 101787921, 593263449, 3457792809, 20153493369, 117463167441, 684625511241, 3990289900041, 23257113888969, 135552393433809, 790057246713849, 4604791086849321

OFFSET

1,1

COMMENTS

Row 4 of A208078

FORMULA

Empirical: a(n) = 5*a(n-1) +5*a(n-2) -a(n-3)

EXAMPLE

Some solutions for n=4

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

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

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

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

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Feb 23 2012

STATUS

approved

editing

#1 by Ron Hardin at Thu Feb 23 06:23:42 EST 2012

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved