

A292171


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


2



16, 47, 117, 327, 988, 3392, 8739, 21372, 53596, 135791, 362528, 887060, 2117839, 4997836, 11731828, 28229247, 66196942, 152418888, 347010327, 784580873, 1794241712, 4064606075, 9109879761, 20253187230, 44774963928, 99368298849, 219638865759, 482519177252
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OFFSET

5,1


COMMENTS

An upjump j occurs at position i in p if p_{i} > p_{i1} 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_{i1}. A downjump j occurs at position i in p if p_{i} < p_{i1} 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_{i1}. First index in the lists is 1 here.


LINKS



EXAMPLE

a(5) = 16: 51234, 51324, 51342, 51423, 51432, 52134, 52314, 52341, 52413, 52431, 53124, 53142, 53214, 53241, 53421, 54321.
a(6) = 47: 512346, 513246, 513426, 513462, 513624, ..., 543216, 543261, 543621, 546321, 564321.


MAPLE

b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
add(b(uj, o+j1, j), j=1..min(t, u))+
add(b(u+j1, oj, j), j=1..min(t, o)))
end:
a:= n> b(0, n, 5)b(0, n, 4):
seq(a(n), n=5..50);


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



