The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Adjacent sequences: A332951 A332952 A332953 * A332955 A332956 A332957 KEYWORD nonn,tabl AUTHOR Seiichi Manyama, Mar 04 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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