cp's OEIS Frontend

A292168 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with two.

%I A292168 #9 Sep 10 2017 14:06:33
%S A292168 1,2,5,9,17,31,57,101,185,333,599,1089,1975,3563,6505,11829,21455,
%T A292168 39257,71641,130403,239193,437677,799127,1468777,2693853,4930871,
%U A292168 9079127,16684737,30605159,56441227,103900161,190934999,352606721,650072239,1196527319,2212404279
%N A292168 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with two.
%C A292168 An up-jump j occurs at position i in p if p_{i} > p_{i-1} and j is the index of p_i in the increasingly sorted list of those elements in {p_{i}, ..., p_{n}} that are larger than p_{i-1}. A down-jump j occurs at position i in p if p_{i} < p_{i-1} and j is the index of p_i in the decreasingly sorted list of those elements in {p_{i}, ..., p_{n}} that are smaller than p_{i-1}. First index in the lists is 1 here.
%H A292168 Alois P. Heinz, <a href="/A292168/b292168.txt">Table of n, a(n) for n = 2..3630</a>
%e A292168 a(2) = 1: 21.
%e A292168 a(3) = 2: 213, 231.
%e A292168 a(4) = 5: 2134, 2314, 2341, 2413, 2431.
%e A292168 a(5) = 9: 21345, 23145, 23415, 23451, 24135, 24153, 24315, 24351, 24531.
%e A292168 a(6) = 17: 213456, 231456, 234156, 234516, 234561, 241356, 241536, 241563, 243156, 243516, 243561, 245316, 245361, 245631, 246315, 246351, 246531.
%p A292168 b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p A292168       add(b(u-j, o+j-1, j), j=1..min(t, u))+
%p A292168       add(b(u+j-1, o-j, j), j=1..min(t, o)))
%p A292168     end:
%p A292168 a:= n-> b(0, n, 2)-b(0, n, 1):
%p A292168 seq(a(n), n=2..50);
%Y A292168 Column k=2 of A291684.
%K A292168 nonn
%O A292168 2,2
%A A292168 _Alois P. Heinz_, Sep 10 2017