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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
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Oct 23 2015
STATUS
approved