A263660 Number of length n arrays of permutations of 0..n-1 with each element moved by -2 to 2 places and with no two consecutive increases or two consecutive decreases.

1, 2, 4, 7, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144, 8192, 12288, 16384, 24576, 32768, 49152, 65536, 98304, 131072, 196608, 262144, 393216, 524288, 786432, 1048576, 1572864, 2097152, 3145728

Offset

1,2

Links

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

Formula

Empirical: a(n) = 2*a(n-2) for n>6.

Conjectures from Colin Barker, Jan 02 2019: (Start)

G.f.: x*(1 + x)*(1 + x - x^2)*(1 + 2*x^2) / (1 - 2*x^2).

a(n) = 3*2^(n/2-1) for n>4 and even.

a(n) = 2^((n-5)/2+3) for n>4 and odd.

(End)

Example

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

Crossrefs

Column 2 of A263666.

Sequence in context: A372098 A090669 A231428 * A215822 A079374 A353579

Adjacent sequences: A263657 A263658 A263659 * A263661 A263662 A263663

Keyword

nonn

Author

R. H. Hardin, Oct 23 2015

Status

approved