cp's OEIS Frontend

A292173 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with seven.

%I A292173 #5 Sep 10 2017 18:00:45
%S A292173 189,627,1633,4291,12146,38795,129520,469662,1281977,3286121,8402785,
%T A292173 21706131,58633404,157849186,439490771,1128233084,2793077829,
%U A292173 6823503775,16758669067,41349963758,101704832977,255372664080,622178277449,1484157011512,3512057801972
%N A292173 Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with seven.
%C A292173 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 A292173 Alois P. Heinz, <a href="/A292173/b292173.txt">Table of n, a(n) for n = 7..2000</a>
%e A292173 a(7) = 189: 7123456, 7132456, 7134256, 7134526, 7134562, 7135246, 7135264, 7135426, 7135462, 7135642, ..., 7534621, 7536214, 7536241, 7536421, 7543216, 7543261, 7543621, 7546321, 7564321, 7654321.
%p A292173 b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p A292173       add(b(u-j, o+j-1, j), j=1..min(t, u))+
%p A292173       add(b(u+j-1, o-j, j), j=1..min(t, o)))
%p A292173     end:
%p A292173 a:= n-> b(0, n, 7)-b(0, n, 6):
%p A292173 seq(a(n), n=7..50);
%Y A292173 Column k=7 of A291684.
%K A292173 nonn
%O A292173 7,1
%A A292173 _Alois P. Heinz_, Sep 10 2017