The On-Line Encyclopedia of Integer Sequences (OEIS)

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A202333

Number of (n+1) X 7 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.
(history; published version)

#8 by Bruno Berselli at Mon May 28 08:09:49 EDT 2018

STATUS

proposed

approved

#7 by Colin Barker at Mon May 28 08:08:44 EDT 2018

STATUS

editing

proposed

#6 by Colin Barker at Mon May 28 08:08:15 EDT 2018

NAME

Number of (n+1)X7 X 7 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.

COMMENTS

Column 6 of A202335.

FORMULA

Empirical: a(n) = (1/2520)*n^7 + (11/720)*n^6 + (167/720)*n^5 + (265/144)*n^4 + (5999/720)*n^3 + (974/45)*n^2 + (4191/140)*n + 19.

Conjectures from Colin Barker, May 28 2018: (Start)

G.f.: x*(81 - 378*x + 854*x^2 - 1148*x^3 + 966*x^4 - 502*x^5 + 148*x^6 - 19*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=5:

CROSSREFS

Cf. A202335.

AUTHOR

R. H. Hardin , Dec 17 2011

STATUS

approved

editing

#5 by Russ Cox at Sat Mar 31 12:36:47 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Dec 17 2011

Discussion

Sat Mar 31

12:36

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

#4 by Ron Hardin at Sat Dec 17 05:52:49 EST 2011

STATUS

editing

approved

#3 by Ron Hardin at Sat Dec 17 05:52:33 EST 2011

LINKS

R. H. Hardin, <a href="/A202333/b202333.txt">Table of n, a(n) for n = 1..210</a>

#2 by Ron Hardin at Sat Dec 17 05:51:52 EST 2011

NAME

allocated for Ron HardinNumber of (n+1)X7 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column

DATA

81, 270, 746, 1796, 3896, 7790, 14588, 25885, 43903, 71658, 113154, 173606, 259694, 379850, 544580, 766823, 1062349, 1450198, 1953162, 2598312, 3417572, 4448342, 5734172, 7325489, 9280379, 11665426, 14556610, 18040266, 22214106, 27188306

OFFSET

1,1

COMMENTS

Column 6 of A202335

FORMULA

Empirical: a(n) = (1/2520)*n^7 + (11/720)*n^6 + (167/720)*n^5 + (265/144)*n^4 + (5999/720)*n^3 + (974/45)*n^2 + (4191/140)*n + 19

EXAMPLE

Some solutions for n=5

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

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

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

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

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

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Dec 17 2011

STATUS

approved

editing

#1 by Ron Hardin at Sat Dec 17 05:42:49 EST 2011

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved