The On-Line Encyclopedia of Integer Sequences (OEIS)

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A202460

Number of (n+2) X 9 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column.
(history; published version)

#8 by Bruno Berselli at Fri Jun 01 05:26:48 EDT 2018

STATUS

proposed

approved

#7 by Colin Barker at Fri Jun 01 05:26:01 EDT 2018

STATUS

editing

proposed

#6 by Colin Barker at Fri Jun 01 05:25:12 EDT 2018

NAME

Number of (n+2)X9 X 9 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column.

COMMENTS

Column 7 of A202461.

FORMULA

Empirical: a(n) = (1/60480)*n^9 + (1/672)*n^8 + (163/3360)*n^7 + (119/144)*n^6 + (24221/2880)*n^5 + (15553/288)*n^4 + (1671487/7560)*n^3 + (282325/504)*n^2 + (404227/420)*n + 937.

Conjectures from Colin Barker, Jun 01 2018: (Start)

G.f.: x*(2744 - 19376*x + 64812*x^2 - 131502*x^3 + 175860*x^4 - 159456*x^5 + 97542*x^6 - 38691*x^7 + 9010*x^8 - 937*x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)

EXAMPLE

Some solutions for 6X6n=4:

CROSSREFS

Cf. A202461.

AUTHOR

R. H. Hardin , Dec 19 2011

STATUS

approved

editing

Discussion

Fri Jun 01

05:26

Colin Barker: I corrected the example, with n=4.

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

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Dec 19 2011

Discussion

Sat Mar 31

12:36

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

#4 by Ron Hardin at Mon Dec 19 11:05:48 EST 2011

STATUS

editing

approved

#3 by Ron Hardin at Mon Dec 19 11:05:45 EST 2011

LINKS

R. H. Hardin, <a href="/A202460/b202460.txt">Table of n, a(n) for n = 1..210</a>

#2 by Ron Hardin at Mon Dec 19 11:05:24 EST 2011

NAME

allocated for Ron HardinNumber of (n+2)X9 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column

DATA

2744, 8064, 21972, 54618, 124740, 264822, 528390, 1000023, 1808746, 3145568, 5286030, 8618736, 13680954, 21202494, 32159196, 47837493, 69911652, 100535440, 142450112, 199110774, 274833336, 374964438, 506076906, 676193475, 895041702

OFFSET

1,1

COMMENTS

Column 7 of A202461

FORMULA

Empirical: a(n) = (1/60480)*n^9 + (1/672)*n^8 + (163/3360)*n^7 + (119/144)*n^6 + (24221/2880)*n^5 + (15553/288)*n^4 + (1671487/7560)*n^3 + (282325/504)*n^2 + (404227/420)*n + 937

EXAMPLE

Some solutions for 6X6

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

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

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

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

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

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

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Dec 19 2011

STATUS

approved

editing

#1 by Ron Hardin at Mon Dec 19 10:56:56 EST 2011

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved