The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A225007 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A225007

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

#41 by Michael De Vlieger at Thu Feb 22 20:31:34 EST 2024

STATUS

reviewed

approved

#40 by Kevin Ryde at Thu Feb 22 19:08:12 EST 2024

STATUS

proposed

reviewed

#39 by Michel Marcus at Thu Feb 22 02:02:53 EST 2024

STATUS

editing

proposed

#38 by Michel Marcus at Thu Feb 22 02:02:38 EST 2024

FORMULA

G.f.: (1 + 10*x + 5*x^2) / (1 - x)^6.

G.f.: (1 + 10*x + 5*x^2) / (1 - x)^6. (End)

STATUS

proposed

editing

#37 by Joerg Arndt at Thu Feb 22 00:47:50 EST 2024

STATUS

editing

proposed

#36 by Joerg Arndt at Thu Feb 22 00:46:57 EST 2024

COMMENTS

Comment from Yasser Arath Chavez Reyes, Feb 21 2024: (Start)

6*a(n-1) + A016061(n) is the partial sum of even-indexed terms of A000537.

a(n-1) + 4*A002415(n+1) is the partial sum of odd-indexed terms of A000332.

(End)

FORMULA

a(n-1) = (2/3)*(A000538(n) + A000537(n) + A000292(n)) - A000292(n). - Yasser Arath Chavez Reyes Feb 21 2024

STATUS

proposed

editing

Discussion

Thu Feb 22

00:47

Joerg Arndt: We have a(n) = (2/15)*n^5 + (7/6)*n^4 + (23/6)*n^3 + (35/6)*n^2 + (121/30)*n + 1. Expressing that as formulas of other polynomials adds nothing of interest.

#35 by Yasser Arath Chavez Reyes at Thu Feb 22 00:03:18 EST 2024

STATUS

editing

proposed

#34 by Yasser Arath Chavez Reyes at Thu Feb 22 00:01:52 EST 2024

COMMENTS

Comment from Yasser Arath Chavez Reyes, Feb 11 21 2024: (Start)

4*a(n-1) - 16+ 4*A005585A002415(n-+1) - A000292(n) is the thrice-repeated partial sum of A001539odd-indexed terms of A000332.

6*a(n-2) + 24*A132366(n-1) = A061167(n).

a(n-1) = (2/3)*(A000538(n) + A000537(n) + A000292(n)) - A000292(n).

FORMULA

a(n-1) = (2/3)*(A000538(n) + A000537(n) + A000292(n)) - A000292(n). - Yasser Arath Chavez Reyes Feb 21 2024

Discussion

Thu Feb 22

00:03

Yasser Arath Chavez Reyes: Sort entries and eliminate confusion

#33 by Joerg Arndt at Fri Feb 16 01:14:45 EST 2024

STATUS

proposed

editing

#32 by Jon E. Schoenfield at Sun Feb 11 19:49:43 EST 2024

STATUS

editing

proposed

Discussion

Tue Feb 13

17:15

Kevin Ryde: Words like "thrice-repeated partial sum" risks ambiguity such as whether the sum is thrice repeated or the terms summed are thrice repeated.  Some formula is clearer.  But all these combinations look fairly unmotivated.  They arise from some problem or calculation?

Fri Feb 16

01:14

Joerg Arndt: I fail to see the point; not the first formula in the formula section