A263899 Number of length n arrays of permutations of 0..n-1 with each element moved by -2 to 2 places and the total absolute value of displacements not greater than 2*(n-1).

1, 2, 6, 13, 31, 73, 172, 399, 932, 2177, 5081, 11853, 27662, 64554, 150639, 351520, 820296, 1914208, 4466904, 10423760, 24324417, 56762346, 132458006, 309097941, 721296815, 1683185225, 3927803988, 9165743599, 21388759708, 49911830577

Offset: 1

Author

R. H. Hardin, Oct 29 2015

Keywords

• nonn

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Column 2 of A263905.

Formula

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

Empirical g.f.: x*(1 + 2*x^2 - x^3) / ((1 - x)*(1 + x)*(1 + x^2)*(1 - 2*x - 2*x^3 + x^5)). - Colin Barker, Jan 03 2019