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A338766 Number of permutations p of [n] such that | |p(i) - p(i-1)| - |p(i+1) - p(i)| | = 1. 1
1, 1, 2, 4, 16, 20, 32, 56, 148, 136, 186, 328, 894, 868, 1196, 1896, 5210, 4936, 6716, 11264, 30046, 28168, 38892, 63272, 169900, 161848, 218944, 367616, 966010, 909192, 1240738, 2100064, 5422442, 5161412, 7027750, 11910404 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..35.

Wikipedia, Permutation

MAPLE

b:= proc(s, x, y) option remember; `if`(s={}, 1, add(

      `if`(x=0 or y=0 or abs(abs(x-y)-abs(y-j))=1,

         b(s minus {j}, y, j), 0), j=s))

    end:

a:= n-> b({$1..n}, 0$2):

seq(a(n), n=0..20);

MATHEMATICA

b[s_, x_, y_] := b[s, x, y] = If[s == {}, 1, Sum[

     If[x == 0 || y == 0 || Abs[Abs[x - y] - Abs[y - j]] == 1,

     b[s ~Complement~ {j}, y, j], 0], {j, s}]];

a[n_] := b[Range[n], 0, 0];

a /@ Range[0, 20] (* Jean-Fran├žois Alcover, Apr 26 2021, after Alois P. Heinz *)

CROSSREFS

Cf. A338765.

Sequence in context: A212202 A102545 A045521 * A242205 A076434 A192150

Adjacent sequences:  A338763 A338764 A338765 * A338767 A338768 A338769

KEYWORD

nonn,more

AUTHOR

Alois P. Heinz, Nov 07 2020

STATUS

approved

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Last modified January 22 15:13 EST 2022. Contains 350481 sequences. (Running on oeis4.)