The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A204278 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A204278

Number of (n+2) X 4 0..2 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..2 introduced in row major order.
(history; published version)

#12 by Bruno Berselli at Thu Jun 07 02:50:59 EDT 2018

STATUS

reviewed

approved

#11 by Michel Marcus at Thu Jun 07 02:28:51 EDT 2018

STATUS

proposed

reviewed

#10 by Jon E. Schoenfield at Thu Jun 07 02:08:18 EDT 2018

STATUS

editing

proposed

#9 by Jon E. Schoenfield at Thu Jun 07 02:08:15 EDT 2018

FORMULA

Empirical: a(n) = 3*a(n-1) - 6*a(n-4) + 4*a(n-6) for n > 9.

EXAMPLE

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

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

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

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

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

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

STATUS

reviewed

editing

#8 by Joerg Arndt at Wed Jun 06 12:06:11 EDT 2018

STATUS

proposed

reviewed

#7 by Colin Barker at Wed Jun 06 11:55:12 EDT 2018

STATUS

editing

proposed

#6 by Colin Barker at Wed Jun 06 11:54:38 EDT 2018

NAME

Number of (n+2)X4 X 4 0..2 arrays with every 3X3 3 X 3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..2 introduced in row major order.

COMMENTS

Column 2 of A204284.

FORMULA

Empirical: a(n) = 3*a(n-1) -6*a(n-4) +4*a(n-6) for n>9.

Empirical g.f.: x*(274 - 200*x - 1001*x^2 - 2402*x^3 + 1604*x^4 + 2850*x^5 + 3772*x^6 - 1792*x^7 - 3072*x^8) / ((1 - x)*(1 - 2*x - 2*x^2)*(1 - 2*x^3)). - Colin Barker, Jun 06 2018

EXAMPLE

Some solutions for n=4:

CROSSREFS

Cf. A204284.

AUTHOR

R. H. Hardin , Jan 13 2012

STATUS

approved

editing

#5 by Russ Cox at Sat Mar 31 12:37:01 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Jan 13 2012

Discussion

Sat Mar 31

12:37

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

#4 by Ron Hardin at Fri Jan 13 20:09:30 EST 2012

STATUS

editing

approved

#3 by Ron Hardin at Fri Jan 13 20:09:26 EST 2012

LINKS

R. H. Hardin, <a href="/A204278/b204278.txt">Table of n, a(n) for n = 1..210</a>