The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A001893 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A001893

Number of permutations of (1,...,n) having n-3 inversions (n>=3).
(history; published version)

#36 by N. J. A. Sloane at Thu Jun 29 19:23:24 EDT 2017

STATUS

proposed

approved

#35 by Rachel Barnett at Thu Jun 29 17:56:51 EDT 2017

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editing

proposed

#34 by Rachel Barnett at Thu Jun 29 17:56:48 EDT 2017

LINKS

R. K. Guy, <a href="/A000707/a000707_2.pdf">Letter to N. J. A. Sloane with attachment, Mar 1988</a>

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approved

editing

#33 by N. J. A. Sloane at Sat Jan 28 14:42:10 EST 2017

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proposed

approved

#32 by Michel Marcus at Fri Jan 27 16:15:18 EST 2017

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editing

proposed

#31 by Michel Marcus at Fri Jan 27 16:15:14 EST 2017

FORMULA

a(n) = 2^(2*n-4)/sqrt(Pi*n)*Q*(1+O(n^{-1})), where Q is a digital search tree constant, Q = 0.2887880951... (see A048651). - corrected by Vaclav Kotesovec, Mar 16 2014

STATUS

proposed

editing

#30 by G. C. Greubel at Fri Jan 27 15:22:25 EST 2017

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editing

proposed

#29 by G. C. Greubel at Fri Jan 27 15:22:15 EST 2017

LINKS

G. C. Greubel, <a href="/A001893/b001893.txt">Table of n, a(n) for n = 3..1000</a>

MAPLE

f := (x, n)->product((1-x^j)/(1-x), j=1..n); seq(coeff(series(f(x, n), x, n+2), x, n-3), n=3..40); # Barbara Haas Margolius, May 31 2001

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms, Maple code, asymptotic formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), May 31 2001

STATUS

approved

editing

#28 by N. J. A. Sloane at Thu Aug 20 18:27:58 EDT 2015

STATUS

editing

approved

#27 by N. J. A. Sloane at Thu Aug 20 18:27:55 EDT 2015

LINKS

E. Netto, <a href="/A000707/a000707_1.pdf">Lehrbuch der Combinatorik</a>, Chapter 4, annotated scanned copy of pages 92-99 only.

STATUS

approved

editing