cp's OEIS Frontend

A292174 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with eight.

%I A292174 #5 Sep 10 2017 18:39:44
%S A292174 683,2400,6471,16817,47123,141118,469662,1609176,5935728,16491722,
%T A292174 43160750,110362553,289385731,767677544,2119594253,5810801164,
%U A292174 16404580983,42548928025,106693231930,263735820713,650860901400,1621682678763,4064296654515,10129808852568
%N A292174 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with eight.
%C A292174 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 A292174 Alois P. Heinz, <a href="/A292174/b292174.txt">Table of n, a(n) for n = 8..2000</a>
%e A292174 a(8) = 683: 81234567, 81324567, 81342567, 81345267, 81345627, 81345672, 81352467, 81352647, 81352674, 81354267, ..., 86473251, 86473521, 86475321, 86543217, 86543271, 86543721, 86547321, 86574321, 86754321, 87654321.
%p A292174 b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p A292174       add(b(u-j, o+j-1, j), j=1..min(t, u))+
%p A292174       add(b(u+j-1, o-j, j), j=1..min(t, o)))
%p A292174     end:
%p A292174 a:= n-> b(0, n, 8)-b(0, n, 7):
%p A292174 seq(a(n), n=8..50);
%Y A292174 Column k=8 of A291684.
%K A292174 nonn
%O A292174 8,1
%A A292174 _Alois P. Heinz_, Sep 10 2017