The On-Line Encyclopedia of Integer Sequences (OEIS)

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A207590

Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 1 vertically.
(history; published version)

#8 by Bruno Berselli at Mon Mar 05 10:00:21 EST 2018

STATUS

proposed

approved

#7 by Colin Barker at Mon Mar 05 09:32:52 EST 2018

STATUS

editing

proposed

#6 by Colin Barker at Mon Mar 05 09:32:31 EST 2018

NAME

Number of 3Xn 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 1 vertically.

COMMENTS

Row 3 of A207589.

FORMULA

Empirical: a(n) = a(n-1) + 3*a(n-2) for n>4.

Conjectures from Colin Barker, Mar 05 2018: (Start)

G.f.: 6*x*(1 + 5*x + x^2 - 4*x^3) / (1 - x - 3*x^2).

a(n) = (2^(1-n)*((1-sqrt(13))^n*(-35+13*sqrt(13)) + (1+sqrt(13))^n*(35+13*sqrt(13)))) / (9*sqrt(13)) for n>2.

(End)

EXAMPLE

Some solutions for n=4:

CROSSREFS

Cf. A207589.

AUTHOR

R. H. Hardin , Feb 19 2012

STATUS

approved

editing

#5 by Russ Cox at Sat Mar 31 12:37:18 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Feb 19 2012

Discussion

Sat Mar 31

12:37

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

#4 by Ron Hardin at Sun Feb 19 07:28:41 EST 2012

STATUS

editing

approved

#3 by Ron Hardin at Sun Feb 19 07:28:38 EST 2012

LINKS

R. H. Hardin, <a href="/A207590/b207590.txt">Table of n, a(n) for n = 1..210</a>

#2 by Ron Hardin at Sun Feb 19 07:28:18 EST 2012

NAME

allocated for Ron HardinNumber of 3Xn 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 1 vertically

DATA

6, 36, 60, 144, 324, 756, 1728, 3996, 9180, 21168, 48708, 112212, 258336, 594972, 1369980, 3154896, 7264836, 16729524, 38524032, 88712604, 204284700, 470422512, 1083276612, 2494544148, 5744373984, 13228006428, 30461128380, 70145147664

OFFSET

1,1

COMMENTS

Row 3 of A207589

FORMULA

Empirical: a(n) = a(n-1) +3*a(n-2) for n>4

EXAMPLE

Some solutions for n=4

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

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

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

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Feb 19 2012

STATUS

approved

editing

#1 by Ron Hardin at Sun Feb 19 07:20:37 EST 2012

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved