The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A242523 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A242523

Number of cyclic arrangements of S={1,2,...,n} such that the difference between any two neighbors is at least 3.
(history; published version)

#17 by N. J. A. Sloane at Wed Oct 24 22:28:03 EDT 2018

STATUS

proposed

approved

#16 by Robert Price at Wed Oct 24 21:24:22 EDT 2018

STATUS

editing

proposed

#15 by Robert Price at Wed Oct 24 21:24:04 EDT 2018

MATHEMATICA

A242523[n_] := Count[Map[lpf, Map[j1f, Permutations[Range[2, n]]]], 0]/2;

j1f[x_] := Join[{1}, x, {1}];

lpf[x_] := Length[Select[Abs[Differences[x]], # < 3 &]];

Table[A242523[n], {n, 1, 10}]

(* OR, a less simple, but more efficient implementation. *)

A242523[n_, perm_, remain_] := Module[{opt, lr, i, new},

If[remain == {},

If[Abs[First[perm] - Last[perm]] >= 3, ct++];

Return[ct],

opt = remain; lr = Length[remain];

For[i = 1, i <= lr, i++,

new = First[opt]; opt = Rest[opt];

If[Abs[Last[perm] - new] < 3, Continue[]];

A242523[n, Join[perm, {new}],

Complement[Range[2, n], perm, {new}]];

];

Return[ct];

];

Table[ct = 0; A242523[n, {1}, Range[2, n]]/2, {n, 1, 11}] (* Robert Price, Oct 24 2018 *)

STATUS

approved

editing

#14 by OEIS Server at Fri Aug 29 04:28:02 EDT 2014

LINKS

Hiroaki Yamanouchi, <a href="/A242523/b242523_1.txt">Table of n, a(n) for n = 1..27</a> (terms a(1)-a(15) from Stanislav Sykora)

#13 by Michel Marcus at Fri Aug 29 04:28:02 EDT 2014

STATUS

reviewed

approved

Discussion

Fri Aug 29

04:28

OEIS Server: Installed new b-file as b242523.txt.  Old b-file is now b242523_1.txt.

#12 by Joerg Arndt at Fri Aug 29 04:10:09 EDT 2014

STATUS

proposed

reviewed

#11 by Joerg Arndt at Fri Aug 29 04:10:03 EDT 2014

STATUS

editing

proposed

#10 by Joerg Arndt at Fri Aug 29 04:10:00 EDT 2014

KEYWORD

nonn,hard,more,changed

STATUS

proposed

editing

#9 by Hiroaki Yamanouchi at Thu Aug 28 23:37:03 EDT 2014

STATUS

editing

proposed

#8 by Hiroaki Yamanouchi at Thu Aug 28 23:36:41 EDT 2014

DATA

0, 0, 0, 0, 0, 0, 1, 11, 125, 1351, 15330, 184846, 2382084, 32795170, 481379278, 7513591430, 124363961357, 2176990766569, 40199252548280, 781143277669538, 15937382209774353, 340696424417421213, 7616192835573406931, 177723017354688250713, 4321711817908214684734

LINKS

Stanislav Sykora, Hiroaki Yamanouchi, <a href="/A242523/b242523_1.txt">Table of n, a(n) for n = 1..27</a> (terms a(1)-a(15</a>) from _Stanislav Sykora_)

EXTENSIONS

a(16)-a(25) from Hiroaki Yamanouchi, Aug 28 2014

STATUS

approved

editing