|
%I #5 Sep 10 2017 17:08:29
%S 16,47,117,327,988,3392,8739,21372,53596,135791,362528,887060,2117839,
%T 4997836,11731828,28229247,66196942,152418888,347010327,784580873,
%U 1794241712,4064606075,9109879761,20253187230,44774963928,99368298849,219638865759,482519177252
%N Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with five.
%C 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 Alois P. Heinz, <a href="/A292171/b292171.txt">Table of n, a(n) for n = 5..3335</a>
%e a(5) = 16: 51234, 51324, 51342, 51423, 51432, 52134, 52314, 52341, 52413, 52431, 53124, 53142, 53214, 53241, 53421, 54321.
%e a(6) = 47: 512346, 513246, 513426, 513462, 513624, ..., 543216, 543261, 543621, 546321, 564321.
%p b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p add(b(u-j, o+j-1, j), j=1..min(t, u))+
%p add(b(u+j-1, o-j, j), j=1..min(t, o)))
%p end:
%p a:= n-> b(0, n, 5)-b(0, n, 4):
%p seq(a(n), n=5..50);
%Y Column k=5 of A291684.
%K nonn
%O 5,1
%A _Alois P. Heinz_, Sep 10 2017
|
