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Revision History for A268783 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

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Number of n X 2 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.
(history; published version)
#8 by Joerg Arndt at Tue Jan 15 09:14:26 EST 2019
STATUS

reviewed

approved

#7 by Michel Marcus at Tue Jan 15 09:11:54 EST 2019
STATUS

proposed

reviewed

#6 by Colin Barker at Tue Jan 15 08:41:11 EST 2019
STATUS

editing

proposed

#5 by Colin Barker at Tue Jan 15 08:40:44 EST 2019
NAME

Number of nX2 n X 2 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

COMMENTS

Column 2 of A268789.

FORMULA

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 2*a(n-3) - 6*a(n-4) - 4*a(n-5) - a(n-6).

Empirical g.f.: x*(1 + 3*x + 4*x^2 + x^3) / (1 - x - 2*x^2 - x^3)^2. - Colin Barker, Jan 15 2019

EXAMPLE

Some solutions for n=4:

CROSSREFS

Cf. Column 2 of A268789.

STATUS

approved

editing

#4 by R. H. Hardin at Sat Feb 13 12:21:53 EST 2016
STATUS

editing

approved

#3 by R. H. Hardin at Sat Feb 13 12:21:50 EST 2016
LINKS

R. H. Hardin, <a href="/A268783/b268783.txt">Table of n, a(n) for n = 1..210</a>

#2 by R. H. Hardin at Sat Feb 13 12:21:33 EST 2016
NAME

allocated for R. H. Hardin

Number of nX2 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

DATA

1, 5, 17, 48, 131, 338, 850, 2091, 5061, 12095, 28608, 67095, 156244, 361652, 832757, 1908885, 4358285, 9915728, 22489147, 50862918, 114743814, 258261695, 580072917, 1300393467, 2910078592, 6501783407, 14504787560, 32313853992, 71896385513

OFFSET

1,2

COMMENTS

Column 2 of A268789.

FORMULA

Empirical: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -6*a(n-4) -4*a(n-5) -a(n-6)

EXAMPLE

Some solutions for n=4

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

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

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

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

CROSSREFS

Cf. A268789.

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin, Feb 13 2016

STATUS

approved

editing

#1 by R. H. Hardin at Sat Feb 13 12:18:10 EST 2016
NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved