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Revision History for A198247

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A198247

Number of 2n X 4 0..4 arrays with values 0..4 introduced in row major order and each element equal to exactly two horizontal and vertical neighbors.
(history; published version)

#8 by Bruno Berselli at Mon May 14 08:25:33 EDT 2018

STATUS

proposed

approved

#7 by Colin Barker at Mon May 14 08:01:15 EDT 2018

STATUS

editing

proposed

#6 by Colin Barker at Mon May 14 08:00:48 EDT 2018

NAME

Number of 2nX4 2n X 4 0..4 arrays with values 0..4 introduced in row major order and each element equal to exactly two horizontal and vertical neighbors.

COMMENTS

Column 2 of A198253.

FORMULA

Empirical: a(n) = 20*a(n-1) -85*a(n-2) -16*a(n-3) +493*a(n-4) -124*a(n-5) -919*a(n-6) +120*a(n-7) +512*a(n-8).

Empirical g.f.: x*(1 - 15*x + 25*x^2 + 126*x^3 - 185*x^4 - 395*x^5 + 287*x^6 + 444*x^7) / ((1 - x)*(1 + x)*(1 - 4*x - x^2 + 8*x^3)*(1 - 16*x + 23*x^2 + 64*x^3)). - Colin Barker, May 14 2018

EXAMPLE

Some solutions for n=3:

CROSSREFS

Cf. A198253.

STATUS

approved

editing

#5 by Russ Cox at Sat Mar 31 12:36:34 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Oct 22 2011

Discussion

Sat Mar 31

12:36

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

#4 by Ron Hardin at Sat Oct 22 14:30:36 EDT 2011

STATUS

editing

approved

#3 by Ron Hardin at Sat Oct 22 14:30:32 EDT 2011

LINKS

R. H. Hardin, <a href="/A198247/b198247.txt">Table of n, a(n) for n = 1..200</a>

#2 by Ron Hardin at Sat Oct 22 14:30:11 EDT 2011

NAME

allocated for Ron HardinNumber of 2nX4 0..4 arrays with values 0..4 introduced in row major order and each element equal to exactly two horizontal and vertical neighbors

DATA

1, 5, 40, 485, 6528, 90641, 1268648, 17794141, 249720000, 3505037833, 49198133832, 690571872597, 9693269289152, 136060470673025, 1909825721373608, 26807451423465421, 376285360845321600, 5281765543824353657

OFFSET

1,2

COMMENTS

Column 2 of A198253

FORMULA

Empirical: a(n) = 20*a(n-1) -85*a(n-2) -16*a(n-3) +493*a(n-4) -124*a(n-5) -919*a(n-6) +120*a(n-7) +512*a(n-8)

EXAMPLE

Some solutions for n=3

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

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

..0..1..1..0....1..1..0..0....2..2..3..3....0..1..1..0....2..2..0..0

..0..0..0..0....1..1..0..0....2..2..3..3....0..0..0..0....2..2..0..0

..2..2..3..3....0..0..1..1....0..0..4..4....1..1..2..2....0..0..3..3

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Oct 22 2011

STATUS

approved

editing

#1 by Ron Hardin at Sat Oct 22 14:27:29 EDT 2011

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved