The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A216837

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A216837

Number of permutations p of {1,...,n} such that at most one element of {p(1),...,p(i-1)} is between p(i) and p(i+1) for all i from 1 to n-1.
(history; published version)

#24 by Alois P. Heinz at Mon Aug 29 10:23:09 EDT 2022

STATUS

editing

approved

#23 by Alois P. Heinz at Sun Aug 28 15:30:09 EDT 2022

FORMULA

a(n) = Sum_{k=0..n-1} A356692(n-1,k) for n >= 1. - _Alois P. Heinz_, Aug 28 2022

#22 by Alois P. Heinz at Sun Aug 28 15:21:32 EDT 2022

FORMULA

a(n) = Sum_{k=0..n-1} A356692(n-1,k) for n >= 1.

CROSSREFS

Cf. A174700, A174701, A174702, A174703, A174704, A174705, A174706, A174707, A174708, A185030, A356692.

STATUS

approved

editing

#21 by Bruno Berselli at Thu Feb 05 04:08:29 EST 2015

STATUS

reviewed

approved

#20 by Joerg Arndt at Thu Feb 05 03:06:37 EST 2015

STATUS

proposed

reviewed

#19 by Jean-François Alcover at Thu Feb 05 02:58:56 EST 2015

STATUS

editing

proposed

#18 by Jean-François Alcover at Thu Feb 05 02:58:50 EST 2015

MATHEMATICA

b[u_, o_] := b[u, o] = If[u+o == 0, 1, Sum[b[Sequence @@ Sort[{o-j, u+j-1}]], {j, 1, Min[2, o]}] + Sum[b[Sequence @@ Sort[{u-j, o+j-1}]], {j, 1, Min[2, u]}]]; a[n_] := If[n == 0, 1, Sum[b[Sequence @@ Sort[{j-1, n-j}]], {j, 1, n}]]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Feb 05 2015, after Alois P. Heinz *)

STATUS

approved

editing

#17 by Vaclav Kotesovec at Sun Feb 23 16:22:22 EST 2014

STATUS

editing

approved

#16 by Vaclav Kotesovec at Sun Feb 23 16:22:11 EST 2014

FORMULA

a(n) ~ c * 4^n, where c = 0.052940679853652794231561081876002147090052503777... - Vaclav Kotesovec, Feb 23 2014

STATUS

approved

editing

#15 by Alois P. Heinz at Thu Oct 03 17:16:45 EDT 2013

STATUS

editing

approved