A263683 T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and with no two consecutive decreases.

1, 1, 2, 1, 2, 3, 1, 2, 5, 5, 1, 2, 5, 12, 8, 1, 2, 5, 17, 26, 13, 1, 2, 5, 17, 53, 58, 21, 1, 2, 5, 17, 70, 155, 131, 34, 1, 2, 5, 17, 70, 277, 429, 295, 55, 1, 2, 5, 17, 70, 349, 1009, 1210, 662, 89, 1, 2, 5, 17, 70, 349, 1658, 3487, 3457, 1487, 144, 1, 2, 5, 17, 70, 349, 2017

Offset

1,3

Comments

Table starts

..1....1....1.....1......1......1......1......1......1......1......1......1

..2....2....2.....2......2......2......2......2......2......2......2......2

..3....5....5.....5......5......5......5......5......5......5......5......5

..5...12...17....17.....17.....17.....17.....17.....17.....17.....17.....17

..8...26...53....70.....70.....70.....70.....70.....70.....70.....70.....70

.13...58..155...277....349....349....349....349....349....349....349....349

.21..131..429..1009...1658...2017...2017...2017...2017...2017...2017...2017

.34..295.1210..3487...7356..11253..13358..13358..13358..13358..13358..13358

.55..662.3457.11708..30374..58743..85403..99377..99377..99377..99377..99377

.89.1487.9948.39905.121676.286327.514631.717372.822041.822041.822041.822041

Links

R. H. Hardin, Table of n, a(n) for n = 1..484

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = 2*a(n-1) +a(n-3) +a(n-4) -a(n-5)

k=3: [order 20]

k=4: [order 70]

Example

Some solutions for n=7 k=4
..2....2....0....0....0....4....1....1....1....3....0....2....2....1....0....2
..0....3....4....2....1....0....5....3....2....4....5....4....1....4....4....0
..3....0....3....1....4....1....2....6....0....5....1....0....5....6....5....1
..4....4....6....4....3....3....3....0....4....6....2....6....0....0....1....6
..5....1....1....5....5....6....0....2....6....0....3....1....4....2....6....3
..1....6....2....6....6....2....4....5....3....1....4....5....6....3....2....5
..6....5....5....3....2....5....6....4....5....2....6....3....3....5....3....4

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A116716.

Diagonal is A049774.

Sequence in context: A029653 A067763 A343863 * A087730 A263736 A126247

Adjacent sequences: A263680 A263681 A263682 * A263684 A263685 A263686

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 23 2015

Status

approved