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A338765 Number of permutations p of [n] such that | |p(i) - p(i-1)| - |p(i+1) - p(i)| | <= 1.

%I A338765 #18 Mar 21 2022 04:46:37
%S A338765 1,1,2,6,18,38,76,162,330,650,1272,2586,5262,10506,20856,41928,83684,
%T A338765 165800,329310,653614,1303388,2584660,5139580,10210912,20288128,
%U A338765 40224174,79824572,158316222,314272812
%N A338765 Number of permutations p of [n] such that | |p(i) - p(i-1)| - |p(i+1) - p(i)| | <= 1.
%H A338765 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%p A338765 b:= proc(s, x, y) option remember; `if`(s={}, 1, add(
%p A338765       `if`(x=0 or y=0 or abs(abs(x-y)-abs(y-j))<=1,
%p A338765          b(s minus {j}, y, j), 0), j=s))
%p A338765     end:
%p A338765 a:= n-> b({$1..n}, 0$2):
%p A338765 seq(a(n), n=0..15);
%t A338765 b[s_, x_, y_] := b[s, x, y] = If[s == {}, 1, Sum[
%t A338765      If[x == 0 || y == 0 || Abs[Abs[x - y] - Abs[y - j]] <= 1,
%t A338765      b[s ~Complement~ {j}, y, j], 0], {j, s}]];
%t A338765 a[n_] := b[Range[n], 0, 0];
%t A338765 a /@ Range[0, 15] (* _Jean-François Alcover_, Apr 26 2021, after _Alois P. Heinz_ *)
%Y A338765 Cf. A295370, A338766.
%K A338765 nonn,more
%O A338765 0,3
%A A338765 _Alois P. Heinz_, Nov 07 2020