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Revision History for A225012 (Underlined text is an addition; strikethrough text is a ~~deletion~~.)
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A225012

Number of 5 X n 0..1 arrays with rows unimodal and columns nondecreasing.
(history; published version)

#10 by R. J. Mathar at Mon May 19 07:47:12 EDT 2014

STATUS

proposed

approved

#9 by Jon E. Schoenfield at Sat May 17 21:35:04 EDT 2014

STATUS

editing

proposed

Discussion

Sun May 18

03:10

Joerg Arndt: "columns nondecreasing" in name appears to be incorrect. Then, all conjectured statements are true.

Mon May 19

07:47

R. J. Mathar: Nondecreasing seems right to me, in fact the A225011 examples have constant
columns, and for 0..1 it's necessarily constant for arrays > 2

#8 by Jon E. Schoenfield at Sat May 17 21:35:02 EDT 2014

NAME

Number of 5 X 5Xnn 0..1 arrays with rows unimodal and columns nondecreasing.

FORMULA

Empirical: a(n) = (1/3628800)*n^10 + (1/80640)*n^9 + (1/3780)*n^8 + (19/5760)*n^7 + (4633/172800)*n^6 + (331/2304)*n^5 + (191249/362880)*n^4 + (24421/20160)*n^3 + (10897/5600)*n^2 + (137/120)*n + 1 = 1 + n*(n+1)* (n^8 + + 44*n^7 + + 916*n^6 + + 11054*n^5 + + 86239*n^4 + + 435086*n^3 + + 1477404*n^2 + + 2918376*n + + 4142880)/ 3628800.

Empirical: G.f.: -x*(x^2- - 3*x+ + 3) *(x^2- - 2*x+ + 2) *(x^2- - x+ + 1) *(x^4- - 4*x^3+ + 5*x^2- - 2*x+ + 1) / (x-1)^11 . - _. - _R. J. Mathar_, May 17 2014

STATUS

reviewed

editing

#7 by R. J. Mathar at Sat May 17 12:20:28 EDT 2014

STATUS

proposed

reviewed

#6 by R. J. Mathar at Sat May 17 12:20:16 EDT 2014

STATUS

editing

proposed

#5 by R. J. Mathar at Sat May 17 12:19:59 EDT 2014

	COMMENTS	`Row 5 of A225010.` `Apparently column 6 of A071920. - R. J. Mathar, May 17 2014`
	FORMULA	`Empirical: a(n) = (1/3628800)n^10 + (1/80640)n^9 + (1/3780)n^8 + (19/5760)n^7 + (4633/172800)n^6 + (331/2304)n^5 + (191249/362880)n^4 + (24421/20160)n^3 + (10897/5600)n^2 + (137/120)n + 1 = 1 + n(n+1) (n^8 +44n^7 +916n^6 +11054n^5 +86239n^4 +435086n^3 +1477404n^2 +2918376n +4142880)/ 3628800.` `Empirical: G.f.: -x(x^2-3x+3) (x^2-2x+2) (x^2-x+1) (x^4-4x^3+5x^2-2x+1) / (x-1)^11 . - R. J. Mathar, May 17 2014`
	AUTHOR	`_R. H. Hardin_ _, Apr 23 2013`
	STATUS	`approved` `editing`

#4 by R. H. Hardin at Tue Apr 23 21:55:22 EDT 2013

STATUS

editing

approved

#3 by R. H. Hardin at Tue Apr 23 21:55:18 EDT 2013

LINKS

R. H. Hardin, <a href="/A225012/b225012.txt">Table of n, a(n) for n = 1..210</a>

#2 by R. H. Hardin at Tue Apr 23 21:54:59 EDT 2013

	NAME	`allocated for R. H. Hardin` `Number of 5Xn 0..1 arrays with rows unimodal and columns nondecreasing`
	DATA	`6, 36, 161, 581, 1792, 4900, 12174, 27966, 60172, 122464, 237590, 442118, 793092, 1377174, 2322967, 3817351, 6126818, 9624964, 14827487, 22436251, 33394208, 48953224, 70757132, 100942636, 142261016, 198223936, 273277036, 373005396`
	OFFSET	`1,1`
	COMMENTS	`Row 5 of A225010`
	FORMULA	`Empirical: a(n) = (1/3628800)n^10 + (1/80640)n^9 + (1/3780)n^8 + (19/5760)n^7 + (4633/172800)n^6 + (331/2304)n^5 + (191249/362880)n^4 + (24421/20160)n^3 + (10897/5600)n^2 + (137/120)n + 1`
	EXAMPLE	`Some solutions for n=3` `..0..0..0....0..1..0....0..1..0....1..0..0....0..0..0....0..0..0....0..0..0` `..1..0..0....0..1..0....1..1..0....1..1..0....0..0..1....0..0..0....0..1..1` `..1..0..0....0..1..0....1..1..1....1..1..0....0..1..1....0..1..0....0..1..1` `..1..1..0....0..1..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....0..1..1....1..1..1....1..1..1`
	KEYWORD	`allocated` `nonn`
	AUTHOR	`R. H. Hardin Apr 23 2013`
	STATUS	`approved` `editing`

#1 by R. H. Hardin at Tue Apr 23 21:47:07 EDT 2013

	NAME	`allocated for R. H. Hardin`
	KEYWORD	`allocated`
	STATUS	`approved`

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Last modified August 30 07:09 EDT 2024. Contains 375532 sequences. (Running on oeis4.)