The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A007754 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A007754

Array (a frieze pattern) defined by a(n,k) = (a(n-1,k)*a(n-1,k+1) - 1) / a(n-2,k+1), read by antidiagonals.
(history; published version)

#23 by Olivier Gérard at Mon Sep 19 10:01:34 EDT 2016

STATUS

proposed

approved

#22 by Michel Marcus at Mon Sep 19 09:57:21 EDT 2016

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editing

proposed

#21 by Michel Marcus at Mon Sep 19 09:57:16 EDT 2016

FORMULA

a(n, k) = (n+k)*a(n-1, k)-a(n-2, k) with a(0, k)=1 and a(-1, k)=0. - Henry Bottomley, Feb 28 2001

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proposed

editing

#20 by Joerg Arndt at Mon Sep 19 09:55:23 EDT 2016

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editing

proposed

#19 by Joerg Arndt at Mon Sep 19 09:55:20 EDT 2016

COMMENTS

Let u be a sequence with u(0)=p, u(1)=q, and u(i)^(i+k) = u(i-1)*u(i+1). Then u(n)= q^a(n-1,k)/p^a(n-2,k+1). - Example for k=1, u(5)=q^7/p^18 and for k=2, u(5)=q^85/p^52. - From __Olivier Gérard_, Sep 19 2016

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proposed

editing

#18 by Olivier Gérard at Mon Sep 19 09:44:34 EDT 2016

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editing

proposed

#17 by Olivier Gérard at Mon Sep 19 04:49:10 EDT 2016

COMMENTS

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approved

editing

#16 by Jon E. Schoenfield at Sun Dec 13 23:40:59 EST 2015

STATUS

editing

approved

#15 by Jon E. Schoenfield at Sun Dec 13 23:40:56 EST 2015

EXAMPLE

1 1 1 1 1 1 1 1 ...

1 2 3 4 5 6 7 ...

1 5 11 19 29 41 ...

2 18 52 110 198 ...

7 85 301 751 ...

STATUS

approved

editing

#14 by Joerg Arndt at Sun Oct 06 14:02:04 EDT 2013

STATUS

proposed

approved