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A332954 Triangle read by rows: T(n,k) is the number of permutations sigma of [n] such that sigma(j)/(j+k) > sigma(j+1)/(j+k+1) for 1 <= j <= n-1. 3
1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 6, 3, 2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1, 19, 8, 5, 3, 2, 1, 1, 1, 30, 13, 7, 5, 3, 2, 1, 1, 1, 60, 21, 12, 7, 5, 3, 2, 1, 1, 1, 108, 38, 17, 11, 7, 5, 3, 2, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,7
COMMENTS
Conjecture: T(2*n+4,n) = A052955(n+2). This is true for n <= 10.
T(n+1,k) is equal to the number of permutations sigma of [n] such that sigma(j)/(j+k) >= sigma(j+1)/(j+k+1) for 1 <= j <= n-1.
LINKS
Seiichi Manyama, Rows n = 0..18, flattened
Mathematics.StackExchange, Why are the numbers of two different permutations the same?, Mar 07 2020.
EXAMPLE
Triangle begins:
n\k | 0 1 2 3 4 5 6 7 8 9 10 11
-----+-----------------------------------------
0 | 1;
1 | 1, 1;
2 | 1, 1, 1;
3 | 2, 1, 1, 1;
4 | 3, 2, 1, 1, 1;
5 | 6, 3, 2, 1, 1, 1;
6 | 9, 5, 3, 2, 1, 1, 1;
7 | 19, 8, 5, 3, 2, 1, 1, 1;
8 | 30, 13, 7, 5, 3, 2, 1, 1, 1;
9 | 60, 21, 12, 7, 5, 3, 2, 1, 1, 1;
10 | 108, 38, 17, 11, 7, 5, 3, 2, 1, 1, 1;
11 | 222, 64, 31, 16, 11, 7, 5, 3, 2, 1, 1, 1;
CROSSREFS
T(n,0) gives A309807.
Cf. A052955.
Sequence in context: A096669 A096591 A316074 * A115568 A072909 A360721
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Mar 04 2020
STATUS
approved

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Last modified July 21 04:02 EDT 2024. Contains 374463 sequences. (Running on oeis4.)