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A338738 Number of permutations p of [n] such that |p(i) - p(i-1)| <= |p(i+1) - p(i)|.

%I A338738 #15 Sep 08 2021 12:40:02
%S A338738 1,1,2,4,6,8,10,14,20,24,32,40,48,70,94,126,162,228,292,386,528,710,
%T A338738 956,1298,1730,2342,3178,4192,5684,7720,10340,14002,18816,25372,34054
%N A338738 Number of permutations p of [n] such that |p(i) - p(i-1)| <= |p(i+1) - p(i)|.
%H A338738 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%e A338738 a(4) = 6: 1234, 2314, 2341, 3214, 3241, 4321.
%p A338738 b:= proc(s, x, y) option remember; `if`(s={}, 1, add(
%p A338738       `if`(x=0 or y=0 or abs(x-y)<=abs(y-j),
%p A338738          b(s minus {j}, y, j), 0), j=s))
%p A338738     end:
%p A338738 a:= n-> b({$1..n}, 0$2):
%p A338738 seq(a(n), n=0..16);
%t A338738 b[s_, x_, y_] := b[s, x, y] = If[s == {}, 1, Sum[If[x == 0 || y == 0 || Abs[x - y] <= Abs[y - j], b[s ~Complement~ {j}, y, j], 0], {j, s}]];
%t A338738 a[n_] := b[Range[n], 0, 0];
%t A338738 Table[Print[n, " ", a[n]]; a[n], {n, 0, 20}] (* _Jean-François Alcover_, Sep 08 2021, after _Alois P. Heinz_ *)
%Y A338738 Cf. A338614.
%K A338738 nonn,more
%O A338738 0,3
%A A338738 _Alois P. Heinz_, Nov 05 2020
%E A338738 a(27)-a(34) from _Bert Dobbelaere_, Nov 15 2020