A211700 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,3

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.

EXAMPLE

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

..1....0....0....0....0

..1....0....0....0....1

..1....0....1....0....1

..1....0....1....1....1

CROSSREFS

Cf. A000110 (column 1), A211694 (column 2), A211695 (column 3).

Sequence in context: A002211 A308947 A175011 * A171840 A132309 A144224

Adjacent sequences: A211697 A211698 A211699 * A211701 A211702 A211703

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 19 2012

STATUS

approved