A338738 - OEIS

%I #15 Sep 08 2021 12:40:02

%S 1,1,2,4,6,8,10,14,20,24,32,40,48,70,94,126,162,228,292,386,528,710,

%T 956,1298,1730,2342,3178,4192,5684,7720,10340,14002,18816,25372,34054

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>

%e a(4) = 6: 1234, 2314, 2341, 3214, 3241, 4321.

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

%p       `if`(x=0 or y=0 or abs(x-y)<=abs(y-j),

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

%p     end:

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

%p seq(a(n), n=0..16);

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

%t Table[Print[n, " ", a[n]]; a[n], {n, 0, 20}] (* _Jean-François Alcover_, Sep 08 2021, after _Alois P. Heinz_ *)

%Y Cf. A338614.

%K nonn,more

%O 0,3

%A _Alois P. Heinz_, Nov 05 2020

%E a(27)-a(34) from _Bert Dobbelaere_, Nov 15 2020