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

Author

R. H. Hardin, Oct 23 2015

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A116716.

Diagonal is A049774.

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]