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A309807 Number of permutations sigma of [n] such that sigma(k)/k > sigma(k+1)/(k+1) for 1 <= k <= n-1. 4
1, 1, 1, 2, 3, 6, 9, 19, 30, 60, 108, 222, 388, 874, 1601, 3244, 6437, 14056, 26545, 57326, 109333, 232751, 481137, 1002039, 1911740, 4261276, 8678424, 17734328, 36186279, 77402058, 154454851, 340848002, 691228119, 1460761640 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
a(n+1) is equal to the number of permutations sigma of [n] such that sigma(k)/k >= sigma(k+1)/(k+1) for 1 <= k <= n-1.
LINKS
Mathematics.StackExchange, Why are the numbers of two different permutations the same?, Mar 07 2020.
EXAMPLE
In case of n = 3.
----+----------
1 | [2, 3, 1]
2 | [3, 2, 1]
In case of n = 4.
----+-------------
1 | [2, 3, 4, 1]
2 | [3, 4, 2, 1]
3 | [4, 3, 2, 1]
PROG
(Ruby)
def A(n)
(1..n).to_a.permutation.select{|i| (1..n - 1).all?{|j| i[j - 1] * (j + 1) > i[j] * j}}.size
end
def A309807(n)
(0..n).map{|i| A(i)}
end
p A309807(10)
CROSSREFS
Row sums of A333310.
Sequence in context: A060172 A193196 A319755 * A003243 A320160 A055873
KEYWORD
nonn,more
AUTHOR
Seiichi Manyama, Mar 03 2020
EXTENSIONS
a(19)-a(22) from Alois P. Heinz, Mar 03 2020
a(23)-a(25) from Giovanni Resta, Mar 04 2020
a(26)-a(33) from Bert Dobbelaere, Mar 15 2020
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)