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Revision History for A208253 (Underlined text is an addition; strikethrough text is a deletion.)

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A208253 Number of n X 3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.
(history; published version)
#9 by Bruno Berselli at Fri Jun 29 08:06:46 EDT 2018
STATUS

proposed

approved

#8 by Colin Barker at Fri Jun 29 06:49:05 EDT 2018
STATUS

editing

proposed

#7 by Colin Barker at Fri Jun 29 06:48:47 EDT 2018
FORMULA

Empirical: a(n) = 22*a(n-1) -) - 16*a(n-2) for n>3.

#6 by Colin Barker at Fri Jun 29 06:47:54 EDT 2018
NAME

Number of n X nX33 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

COMMENTS

Column 3 of A208258.

FORMULA

Empirical: a(n) = 22*a(n-1) -16*a(n-2) for n>3.

Conjectures from Colin Barker, Jun 29 2018: (Start)

G.f.: x*(1 - 2*x)*(5 - 4*x) / (1 - 22*x + 16*x^2).

a(n) = (1/32)*sqrt(3/35)*((11-sqrt(105))^n*(-13+sqrt(105)) + (11+sqrt(105))^n*(13+sqrt(105))) for n>1.

(End)

EXAMPLE

Some solutions for n=4:

CROSSREFS

Cf. A208258.

AUTHOR

_R. H. Hardin_ _, Feb 24 2012

STATUS

approved

editing

#5 by Russ Cox at Sat Mar 31 12:37:22 EDT 2012
AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Feb 24 2012

Discussion
Sat Mar 31 12:37
OEIS Server: https://oeis.org/edit/global/875
#4 by Ron Hardin at Fri Feb 24 18:55:55 EST 2012
STATUS

editing

approved

#3 by Ron Hardin at Fri Feb 24 18:55:52 EST 2012
LINKS

R. H. Hardin, <a href="/A208253/b208253.txt">Table of n, a(n) for n = 1..210</a>

#2 by Ron Hardin at Fri Feb 24 18:55:31 EST 2012
NAME

allocatedNumber of nX3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward foror Ronupward Hardinneighbors

DATA

5, 96, 2040, 43344, 920928, 19566912, 415737216, 8833148160, 187677464064, 3987573838848, 84723785029632, 1800122089230336, 38247105402593280, 812634365429366784, 17266002353004576768, 366849901919230820352

OFFSET

1,1

COMMENTS

Column 3 of A208258

FORMULA

Empirical: a(n) = 22*a(n-1) -16*a(n-2) for n>3

EXAMPLE

Some solutions for n=4

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

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

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

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

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Feb 24 2012

STATUS

approved

editing

#1 by Ron Hardin at Fri Feb 24 18:53:10 EST 2012
NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved

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Last modified August 29 13:55 EDT 2024. Contains 375517 sequences. (Running on oeis4.)