The On-Line Encyclopedia of Integer Sequences (OEIS)

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A202526

Number of (n+2) X 4 binary arrays avoiding patterns 000 and 101 in rows, columns and nw-to-se diagonals.
(history; published version)

#8 by Bruno Berselli at Fri Jun 01 06:02:13 EDT 2018

STATUS

proposed

approved

#7 by Colin Barker at Fri Jun 01 05:51:13 EDT 2018

STATUS

editing

proposed

#6 by Colin Barker at Fri Jun 01 05:50:48 EDT 2018

NAME

Number of (n+2)X4 X 4 binary arrays avoiding patterns 000 and 101 in rows, columns and nw-to-se diagonals.

COMMENTS

Column 2 of A202532.

FORMULA

Empirical: a(n) = 2*a(n-1) +2*a(n-3) -2*a(n-4) -2*a(n-5) +a(n-7) for n>9.

Empirical g.f.: x*(198 + 122*x + 48*x^2 - 332*x^3 - 203*x^4 + 46*x^5 + 97*x^6 + 11*x^7 + 4*x^8) / ((1 - x)*(1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - Colin Barker, Jun 01 2018

EXAMPLE

Some solutions for n=3:

CROSSREFS

Cf. A202532.

AUTHOR

R. H. Hardin , Dec 20 2011

STATUS

approved

editing

#5 by Russ Cox at Sat Mar 31 12:36:48 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Dec 20 2011

Discussion

Sat Mar 31

12:36

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

#4 by Ron Hardin at Tue Dec 20 16:22:07 EST 2011

STATUS

editing

approved

#3 by Ron Hardin at Tue Dec 20 16:22:04 EST 2011

LINKS

R. H. Hardin, <a href="/A202526/b202526.txt">Table of n, a(n) for n = 1..210</a>

#2 by Ron Hardin at Tue Dec 20 16:21:37 EST 2011

NAME

allocated for Ron HardinNumber of (n+2)X4 binary arrays avoiding patterns 000 and 101 in rows, columns and nw-to-se diagonals

DATA

198, 518, 1084, 2232, 4901, 10584, 22525, 48429, 104282, 223728, 480328, 1032213, 2217044, 4761249, 10227241, 21967770, 47183252, 101344728, 217680229, 467553984, 1004256629, 2157044997, 4633115818, 9951459720, 21374732936

OFFSET

1,1

COMMENTS

Column 2 of A202532

FORMULA

Empirical: a(n) = 2*a(n-1) +2*a(n-3) -2*a(n-4) -2*a(n-5) +a(n-7) for n>9

EXAMPLE

Some solutions for n=3

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

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

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

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

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

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Dec 20 2011

STATUS

approved

editing

#1 by Ron Hardin at Tue Dec 20 16:19:04 EST 2011

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved