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%I #10 Jan 02 2019 23:16:46
%S 1,2,4,10,22,40,70,133,254,482,902,1710,3214,6094,11446,21702,40766,
%T 77294,145190,275286,517102,980446,1841686,3491910,6559262,12436622,
%U 23361158,44293686,83201998,157754302,296328310,561850278,1055388926
%N Number of length n arrays of permutations of 0..n-1 with each element moved by -3 to 3 places and with no two consecutive increases or two consecutive decreases.
%H R. H. Hardin, <a href="/A263661/b263661.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-2) + 2*a(n-4) for n>12.
%F Empirical g.f.: x*(1 + x)*(1 + x + 4*x^3 + 4*x^4 + 2*x^5 - 6*x^6 - x^7 + x^8 + 2*x^9 - 2*x^10) / (1 - 3*x^2 - 2*x^4). - _Colin Barker_, Jan 02 2019
%e Some solutions for n=7:
%e ..3....1....3....2....1....2....0....1....2....1....3....1....0....3....2....1
%e ..1....3....0....1....3....4....2....0....0....2....1....0....4....1....1....4
%e ..5....0....2....4....0....0....1....4....5....0....4....5....1....2....3....0
%e ..0....5....1....0....4....3....6....2....1....4....0....3....3....0....0....3
%e ..4....2....5....6....2....1....3....6....4....3....5....4....2....5....5....2
%e ..2....6....4....3....6....6....5....3....3....6....2....2....6....4....4....6
%e ..6....4....6....5....5....5....4....5....6....5....6....6....5....6....6....5
%Y Column 3 of A263666.
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 23 2015