The On-Line Encyclopedia of Integer Sequences (OEIS)

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A205830

Number of (n+1) X 3 0..2 arrays with the number of clockwise edge increases in every 2 X 2 subblock equal to two.
(history; published version)

#9 by Alois P. Heinz at Wed Jun 13 03:23:55 EDT 2018

STATUS

reviewed

approved

#8 by Michel Marcus at Wed Jun 13 02:56:46 EDT 2018

STATUS

proposed

reviewed

#7 by Colin Barker at Wed Jun 13 02:54:28 EDT 2018

STATUS

editing

proposed

#6 by Colin Barker at Wed Jun 13 02:53:46 EDT 2018

NAME

Number of (n+1)X3 X 3 0..2 arrays with the number of clockwise edge increases in every 2X2 2 X 2 subblock equal to two.

COMMENTS

Column 2 of A205836.

FORMULA

Empirical: a(n) = 7*a(n-1) -8*a(n-2) +6*a(n-3) for n>4.

Empirical g.f.: 3*x*(37 - 49*x + 40*x^2 + 2*x^3) / (1 - 7*x + 8*x^2 - 6*x^3). - Colin Barker, Jun 13 2018

EXAMPLE

Some solutions for n=4:

CROSSREFS

Cf. A205836.

AUTHOR

R. H. Hardin , Feb 01 2012

STATUS

approved

editing

#5 by Russ Cox at Sat Mar 31 12:37:07 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Feb 01 2012

Discussion

Sat Mar 31

12:37

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

#4 by Ron Hardin at Wed Feb 01 11:38:33 EST 2012

STATUS

editing

approved

#3 by Ron Hardin at Wed Feb 01 11:38:30 EST 2012

LINKS

R. H. Hardin, <a href="/A205830/b205830.txt">Table of n, a(n) for n = 1..210</a>

#2 by Ron Hardin at Wed Feb 01 11:38:12 EST 2012

NAME

allocated for Ron HardinNumber of (n+1)X3 0..2 arrays with the number of clockwise edge increases in every 2X2 subblock equal to two

DATA

111, 630, 3642, 21126, 122526, 710526, 4120230, 23892558, 138549222, 803425470, 4658939862, 27016470606, 156664328166, 908472171486, 5268089398710, 30548834388078, 177147958555782, 1027253571178110, 5956884336128982

OFFSET

1,1

COMMENTS

Column 2 of A205836

FORMULA

Empirical: a(n) = 7*a(n-1) -8*a(n-2) +6*a(n-3) for n>4

EXAMPLE

Some solutions for n=4

..0..1..1....1..2..0....2..1..1....0..0..1....2..1..0....2..1..1....0..2..1

..2..0..2....1..0..1....1..0..2....2..1..2....0..2..1....1..0..2....2..1..2

..2..1..0....2..1..0....2..1..0....0..2..0....1..0..2....2..1..0....0..2..0

..1..0..1....0..2..1....0..2..1....2..1..2....2..1..0....0..2..1....2..0..2

..0..1..2....2..1..2....1..0..2....1..2..1....0..2..1....2..0..2....0..1..0

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Feb 01 2012

STATUS

approved

editing

#1 by Ron Hardin at Wed Feb 01 11:35:55 EST 2012

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved