A217891 T(n,k) is the number of n element 1..n arrays with each element the minimum of k adjacent elements of a permutation of 1..n+k-1 of n+k-1 elements.

1, 1, 2, 1, 3, 6, 1, 3, 10, 24, 1, 3, 11, 40, 120, 1, 3, 11, 44, 182, 720, 1, 3, 11, 45, 192, 938, 5040, 1, 3, 11, 45, 196, 892, 5424, 40320, 1, 3, 11, 45, 197, 898, 4400, 34788, 362880, 1, 3, 11, 45, 197, 902, 4272, 23086, 244544, 3628800, 1, 3, 11, 45, 197, 903, 4274, 21002, 129250, 1865144, 39916800

Offset

1,3

Links

R. H. Hardin, Table of n, a(n) for n = 1..159

Example

Table starts:
.........1.........1........1........1........1........1.......1......1......1
.........2.........3........3........3........3........3.......3......3......3
.........6........10.......11.......11.......11.......11......11.....11.....11
........24........40.......44.......45.......45.......45......45.....45.....45
.......120.......182......192......196......197......197.....197....197....197
.......720.......938......892......898......902......903.....903....903....903
......5040......5424.....4400.....4272.....4274.....4278....4279...4279...4279
.....40320.....34788....23086....21002....20790....20788...20792..20793..20793
....362880....244544...129250...106564...103354...103050..103044.103048.103049
...3628800...1865144...773868...558780...523786...519268..518864.518854
..39916800..15312976..4953208..3037926..2703206..2653278.2647244
.479001600.134495328.33778104.17203726.14210824.13725388
Some solutions for n=4 and k=4:
..1....2....3....1....2....2....1....1....1....2....1....1....4....2....2....3
..2....4....4....1....4....3....3....3....1....1....1....1....3....2....2....3
..3....1....2....3....3....4....4....2....2....1....3....4....1....1....4....2
..3....1....1....3....1....1....2....2....3....1....4....3....1....1....1....1

Crossrefs

Diagonal is A001003.

Sequence in context: A081520 A238955 A238968 * A322044 A010251 A051537

Adjacent sequences: A217888 A217889 A217890 * A217892 A217893 A217894

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 14 2012

Status

approved