The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A183436

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Number of n X 3 binary arrays with every 1 having exactly one king-move neighbor equal to 1.
(history; published version)

#9 by Joerg Arndt at Thu Mar 29 05:30:41 EDT 2018

STATUS

reviewed

approved

#8 by Michel Marcus at Thu Mar 29 05:28:52 EDT 2018

STATUS

proposed

reviewed

#7 by Colin Barker at Thu Mar 29 05:26:17 EDT 2018

STATUS

editing

proposed

#6 by Colin Barker at Thu Mar 29 05:25:47 EDT 2018

NAME

Number of nX3 n X 3 binary arrays with every 1 having exactly one king-move neighbor equal to 1.

COMMENTS

Column 3 of A183442.

FORMULA

Empirical: a(n) = a(n-1) + 3*a(n-2) + 8*a(n-3) - a(n-4) - 2*a(n-5) - 2*a(n-6).

Empirical g.f.: x*(3 + 10*x + 7*x^2 - 3*x^3 - 4*x^4 - 2*x^5) / (1 - x - 3*x^2 - 8*x^3 + x^4 + 2*x^5 + 2*x^6). - Colin Barker, Mar 29 2018

EXAMPLE

Some solutions for 5X35 X 3.

CROSSREFS

Cf. A183442.

AUTHOR

R. H. Hardin , Jan 04 2011

STATUS

approved

editing

#5 by Russ Cox at Sat Mar 31 12:35:51 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Jan 04 2011

Discussion

Sat Mar 31

12:35

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

#4 by Ron Hardin at Tue Jan 04 19:10:07 EST 2011

STATUS

proposed

approved

#3 by Ron Hardin at Tue Jan 04 19:09:47 EST 2011

LINKS

R. H. Hardin, <a href="/A183436/b183436.txt">Table of n, a(n) for n = 1..200</a>

#2 by Ron Hardin at Tue Jan 04 19:09:09 EST 2011

NAME

allocated for Ron HardinNumber of nX3 binary arrays with every 1 having exactly one king-move neighbor equal to 1

DATA

3, 13, 29, 89, 273, 751, 2221, 6485, 18647, 54395, 157947, 457879, 1330821, 3863375, 11214839, 32568969, 94558013, 274542857, 797165417, 2314532695, 6720246173, 19512370773, 56654003695, 164495136155, 477612471027, 1386747980543

OFFSET

1,1

COMMENTS

Column 3 of A183442

FORMULA

Empirical: a(n)=a(n-1)+3*a(n-2)+8*a(n-3)-a(n-4)-2*a(n-5)-2*a(n-6)

EXAMPLE

Some solutions for 5X3

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

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

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

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

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

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Jan 04 2011

STATUS

approved

proposed

#1 by Ron Hardin at Tue Jan 04 19:02:50 EST 2011

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved