A211700 T(n,k)=Number of nonnegative integer arrays of length n+2k-2 with new values introduced in order 0 upwards and every value appearing only in runs of at least k.
1, 1, 2, 1, 2, 5, 1, 2, 3, 15, 1, 2, 3, 6, 52, 1, 2, 3, 4, 11, 203, 1, 2, 3, 4, 7, 23, 877, 1, 2, 3, 4, 5, 12, 47, 4140, 1, 2, 3, 4, 5, 8, 19, 103, 21147, 1, 2, 3, 4, 5, 6, 13, 33, 226, 115975, 1, 2, 3, 4, 5, 6, 9, 20, 59, 518, 678570, 1, 2, 3, 4, 5, 6, 7, 14, 29, 102, 1200, 4213597, 1, 2, 3, 4
Offset: 1
Examples
Table starts ..........1.....1....1...1...1...1..1..1..1..1..1..1..1..1 ..........2.....2....2...2...2...2..2..2..2..2..2..2..2..2 ..........5.....3....3...3...3...3..3..3..3..3..3..3..3..3 .........15.....6....4...4...4...4..4..4..4..4..4..4..4..4 .........52....11....7...5...5...5..5..5..5..5..5..5..5..5 ........203....23...12...8...6...6..6..6..6..6..6..6..6..6 ........877....47...19..13...9...7..7..7..7..7..7..7..7..7 .......4140...103...33..20..14..10..8..8..8..8..8..8..8..8 ......21147...226...59..29..21..15.11..9..9..9..9..9..9..9 .....115975...518..102..45..30..22.16.12.10.10.10.10.10.10 .....678570..1200..182..73..41..31.23.17.13.11.11.11.11.11 ....4213597..2867..334.118..59..42.32.24.18.14.12.12.12.12 ...27644437..6946..608.185..89..55.43.33.25.19.15.13.13.13 ..190899322.17234.1121.294.136..75.56.44.34.26.20.16.14.14 .1382958545.43393.2109.480.205.107.71.57.45.35.27.21.17.15 All solutions for n=5 k=4 ..0....0....0....0....0 ..0....0....0....0....0 ..0....0....0....0....0 ..0....0....0....0....0 ..1....0....0....0....0 ..1....0....0....0....1 ..1....0....1....0....1 ..1....0....1....1....1 ..1....0....1....1....1 ..1....0....1....1....1 ..1....0....1....1....1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..9999
- Beáta Bényi, Toufik Mansour, and José L. Ramírez, Set partitions and non-crossing partitions with l-neighbors and l-isolated elements, Australasian J. Comb. (2022) Vol. 84, No. 2, 325-340.