The On-Line Encyclopedia of Integer Sequences (OEIS)

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A202935

Number of (n+3) X 7 binary arrays with consecutive windows of four bits considered as a binary number nondecreasing in every row and column.
(history; published version)

#9 by Susanna Cuyler at Sun Jun 03 07:57:30 EDT 2018

STATUS

reviewed

approved

#8 by Joerg Arndt at Sun Jun 03 07:40:45 EDT 2018

STATUS

proposed

reviewed

#7 by Colin Barker at Sun Jun 03 05:24:15 EDT 2018

STATUS

editing

proposed

#6 by Colin Barker at Sun Jun 03 05:23:38 EDT 2018

NAME

Number of (n+3)X7 X 7 binary arrays with consecutive windows of four bits considered as a binary number nondecreasing in every row and column.

COMMENTS

Column 4 of A202939.

FORMULA

Empirical: a(n) = (1/210)*n^7 + (11/20)*n^6 + (81/5)*n^5 + (1713/8)*n^4 + (90179/60)*n^3 + (337713/40)*n^2 + (15214631/420)*n + 83919.

Conjectures from Colin Barker, Jun 03 2018: (Start)

G.f.: x*(130321 - 836423*x + 2330681*x^2 - 3638908*x^3 + 3428986*x^4 - 1947234*x^5 + 616520*x^6 - 83919*x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

EXAMPLE

Some solutions for n=1:

CROSSREFS

Cf. A202939.

AUTHOR

R. H. Hardin , Dec 26 2011

STATUS

approved

editing

#5 by Russ Cox at Sat Mar 31 12:36:53 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Dec 26 2011

Discussion

Sat Mar 31

12:36

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

#4 by Ron Hardin at Mon Dec 26 10:21:51 EST 2011

STATUS

editing

approved

#3 by Ron Hardin at Mon Dec 26 10:21:48 EST 2011

LINKS

R. H. Hardin, <a href="/A202935/b202935.txt">Table of n, a(n) for n = 1..210</a>

#2 by Ron Hardin at Mon Dec 26 10:21:30 EST 2011

NAME

allocated for Ron HardinNumber of (n+3)X7 binary arrays with consecutive windows of four bits considered as a binary number nondecreasing in every row and column

DATA

130321, 206145, 330853, 533832, 857408, 1360328, 2121734, 3245653, 4866027, 7152307, 10315635, 14615638, 20367858, 27951842, 37819916, 50506667, 66639157, 86947893, 112278577, 143604660, 182040724, 228856716, 285493058, 353576657

OFFSET

1,1

COMMENTS

Column 4 of A202939

FORMULA

Empirical: a(n) = (1/210)*n^7 + (11/20)*n^6 + (81/5)*n^5 + (1713/8)*n^4 + (90179/60)*n^3 + (337713/40)*n^2 + (15214631/420)*n + 83919

EXAMPLE

Some solutions for n=1

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

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

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

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

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Dec 26 2011

STATUS

approved

editing

#1 by Ron Hardin at Mon Dec 26 10:17:11 EST 2011

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved