cp's OEIS Frontend

A292172 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with six.

%I A292172 #5 Sep 10 2017 17:27:12
%S A292172 52,166,425,1116,3392,10872,38795,102634,260334,651704,1707641,
%T A292172 4477199,12277412,30970764,75239813,181934538,440594545,1063081418,
%U A292172 2625678546,6286974074,14803016600,34534616815,80129926919,185059517397,431845849360,997735570874
%N A292172 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with six.
%C A292172 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 A292172 Alois P. Heinz, <a href="/A292172/b292172.txt">Table of n, a(n) for n = 6..2000</a>
%e A292172 a(6) = 52: 612345, 613245, 613425, 613452, 613524, 613542, 614235, 614253, 614325, 614352, 614532, 615234, 615243, 615324, 615342, 615432, 621345, 623145, 623415, 623451, 624135, 624153, 624315, 624351, 624531, 625134, 625143, 625314, 625341, 625431, 631245, 631425, 631452, 632145, 632415, 632451, 634215, 634251, 634521, 635214, 635241, 635421, 642135, 642315, 642351, 642513, 642531, 643215, 643251, 643521, 645321, 654321.
%p A292172 b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p A292172       add(b(u-j, o+j-1, j), j=1..min(t, u))+
%p A292172       add(b(u+j-1, o-j, j), j=1..min(t, o)))
%p A292172     end:
%p A292172 a:= n-> b(0, n, 6)-b(0, n, 5):
%p A292172 seq(a(n), n=6..50);
%Y A292172 Column k=6 of A291684.
%K A292172 nonn
%O A292172 6,1
%A A292172 _Alois P. Heinz_, Sep 10 2017