A263660 - OEIS

%I #12 Jan 02 2019 11:29:54

%S 1,2,4,7,8,12,16,24,32,48,64,96,128,192,256,384,512,768,1024,1536,

%T 2048,3072,4096,6144,8192,12288,16384,24576,32768,49152,65536,98304,

%U 131072,196608,262144,393216,524288,786432,1048576,1572864,2097152,3145728

%N 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.

%H R. H. Hardin, <a href="/A263660/b263660.txt">Table of n, a(n) for n = 1..210</a>

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

%F Conjectures from _Colin Barker_, Jan 02 2019: (Start)

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

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

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

%F (End)

%e All solutions for n=7:

%e ..0....1....1....1....0....2....2....0....1....1....0....1....2....1....1....2

%e ..3....2....0....3....2....0....0....3....0....0....2....2....0....3....0....0

%e ..1....0....3....0....1....4....3....1....3....4....1....0....3....0....4....4

%e ..5....5....2....5....5....1....1....4....2....2....4....4....1....4....2....1

%e ..2....3....6....2....3....6....5....2....5....5....3....3....6....2....6....5

%e ..6....6....4....6....6....3....4....6....4....3....6....6....4....6....3....3

%e ..4....4....5....4....4....5....6....5....6....6....5....5....5....5....5....6

%Y Column 2 of A263666.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 23 2015