A263905 T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and the total absolute value of displacements not greater than 2*(n-1).

1, 1, 2, 1, 2, 3, 1, 2, 6, 5, 1, 2, 6, 13, 8, 1, 2, 6, 20, 31, 13, 1, 2, 6, 20, 61, 73, 21, 1, 2, 6, 20, 76, 185, 172, 34, 1, 2, 6, 20, 76, 269, 577, 399, 55, 1, 2, 6, 20, 76, 300, 979, 1788, 932, 89, 1, 2, 6, 20, 76, 300, 1189, 3552, 5540, 2177, 144, 1, 2, 6, 20, 76, 300, 1252

Offset: 1

Author

R. H. Hardin, Oct 29 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....6.....6.....6.....6.....6.....6......6......6......6......6......6

..5...13....20....20....20....20....20.....20.....20.....20.....20.....20

..8...31....61....76....76....76....76.....76.....76.....76.....76.....76

.13...73...185...269...300...300...300....300....300....300....300....300

.21..172...577...979..1189..1252..1252...1252...1252...1252...1252...1252

.34..399..1788..3552..4701..5197..5324...5324...5324...5324...5324...5324

.55..932..5540.13068.18754.21735.22869..23124..23124..23124..23124..23124

.89.2177.17165.47999.75243.91151.98497.101037.101548.101548.101548.101548

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..617

Crossrefs

Column 1 is A000045(n+1).

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +2*a(n-3) +a(n-4) -3*a(n-5) -2*a(n-7) +a(n-9)