The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A332852

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A332852

Number of entries in the third cycles of all permutations of [n] when cycles are ordered by decreasing lengths.
(history; published version)

#14 by Alois P. Heinz at Sun Dec 12 10:04:58 EST 2021

STATUS

editing

approved

#13 by Alois P. Heinz at Sun Dec 12 09:52:14 EST 2021

FORMULA

a(n) = Sum_{k=0..floor(n/3)} k * A350015(n,k). - Alois P. Heinz, Dec 12 2021

CROSSREFS

Cf. A350015.

STATUS

approved

editing

#12 by OEIS Server at Mon Mar 02 07:47:10 EST 2020

LINKS

Alois P. Heinz, <a href="/A332852/b332852_1.txt">Table of n, a(n) for n = 3..450</a>

#11 by Alois P. Heinz at Mon Mar 02 07:47:10 EST 2020

STATUS

editing

approved

Discussion

Mon Mar 02

07:47

OEIS Server: Installed new b-file as b332852.txt.  Old b-file is now b332852_1.txt.

#10 by Alois P. Heinz at Mon Mar 02 07:47:07 EST 2020

LINKS

Alois P. Heinz, <a href="/A332852/b332852_1.txt">Table of n, a(n) for n = 3..175450</a>

STATUS

approved

editing

#9 by Michel Marcus at Sun Mar 01 06:48:08 EST 2020

STATUS

reviewed

approved

#8 by Joerg Arndt at Sun Mar 01 06:36:33 EST 2020

STATUS

proposed

reviewed

#7 by Jean-François Alcover at Sun Mar 01 05:17:52 EST 2020

STATUS

editing

proposed

#6 by Jean-François Alcover at Sun Mar 01 05:17:49 EST 2020

MATHEMATICA

b[n_, l_] := b[n, l] = If[n == 0, l[[3]], Sum[(j-1)! b[n-j, ReverseSort[ Append[l, j]][[1 ;; 3]]] Binomial[n - 1, j - 1], {j, 1, n}]];

a[n_] := b[n, {0, 0, 0}];

a /@ Range[3, 23] (* Jean-François Alcover, Mar 01 2020, after Alois P. Heinz *)

STATUS

approved

editing

#5 by Alois P. Heinz at Wed Feb 26 23:22:07 EST 2020

STATUS

editing

approved