The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A198638

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A198638

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

#9 by Bruno Berselli at Tue May 15 06:42:06 EDT 2018

STATUS

proposed

approved

#8 by Colin Barker at Tue May 15 06:41:57 EDT 2018

STATUS

editing

proposed

#7 by Colin Barker at Tue May 15 06:41:21 EDT 2018

NAME

Number of 2nX2 2n X 2 0..2 arrays with values 0..2 introduced in row major order and each element equal to an even number of horizontal and vertical neighbors.

COMMENTS

Column 1 of A198642.

FORMULA

Empirical: a(n) = 12*a(n-1) -16*a(n-2) for n>3.

Conjectures from Colin Barker, May 15 2018: (Start)

G.f.: 4*x*(1 - x)*(1 - 2*x) / (1 - 12*x + 16*x^2).

a(n) = ((6 - 2*sqrt(5))^n*(-5+3*sqrt(5)) + (2*(3+sqrt(5)))^n*(5+3*sqrt(5))) / (16*sqrt(5)) for n>1.

(End)

EXAMPLE

Some solutions for n=3:

CROSSREFS

Cf. A198642.

AUTHOR

R. H. Hardin , Oct 27 2011

STATUS

approved

editing

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

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Oct 27 2011

Discussion

Sat Mar 31

12:36

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

#5 by Ron Hardin at Thu Oct 27 19:45:00 EDT 2011

STATUS

editing

approved

#4 by Ron Hardin at Thu Oct 27 19:44:56 EDT 2011

LINKS

R. H. Hardin, <a href="/A198638/b198638.txt">Table of n, a(n) for n = 1..200</a>

#3 by Ron Hardin at Thu Oct 27 19:44:37 EDT 2011

NAME

allocated for Ron HardinNumber of 2nX2 0..2 arrays with values 0..2 introduced in row major order and each element equal to an even number of horizontal and vertical neighbors

DATA

4, 36, 376, 3936, 41216, 431616, 4519936, 47333376, 495681536, 5190844416, 54359228416, 569257230336, 5961339109376, 62427953627136, 653754017775616, 6846200955273216, 71694347178868736, 750792950862053376

OFFSET

1,1

COMMENTS

Column 1 of A198642

FORMULA

Empirical: a(n) = 12*a(n-1) -16*a(n-2) for n>3

EXAMPLE

Some solutions for n=3

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

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

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

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

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

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

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Oct 27 2011

STATUS

approved

editing

#2 by Ron Hardin at Thu Oct 27 19:42:58 EDT 2011

KEYWORD

allocating

allocated

#1 by Ron Hardin at Thu Oct 27 19:42:58 EDT 2011

NAME

allocated for Ron Hardin

KEYWORD

allocating

STATUS

approved