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A263678 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 decreases.

%I A263678 #7 Sep 07 2022 11:47:44
%S A263678 1,2,5,17,53,155,429,1210,3457,9948,28528,81636,233344,667390,1909626,
%T A263678 5464861,15637212,44741387,128011961,366269502,1047988385,2998562936,
%U A263678 8579622673,24548350663,70238679485,200969734254,575022887468
%N A263678 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 decreases.
%C A263678 Column 3 of A263683.
%H A263678 R. H. Hardin, <a href="/A263678/b263678.txt">Table of n, a(n) for n = 1..210</a>
%F A263678 Empirical: a(n) = a(n-1) +3*a(n-2) +3*a(n-3) +5*a(n-4) +9*a(n-5) +22*a(n-6) -21*a(n-8) -13*a(n-9) +2*a(n-10) +3*a(n-11) -15*a(n-12) +7*a(n-14) +5*a(n-15) -a(n-16) -2*a(n-17) +3*a(n-18) -a(n-20).
%e A263678 Some solutions for n=7
%e A263678 ..1....0....2....0....0....0....1....0....0....2....0....2....1....1....3....0
%e A263678 ..0....4....0....1....2....1....3....2....2....0....1....1....4....3....1....1
%e A263678 ..5....5....1....3....3....2....0....1....1....4....5....4....0....4....5....3
%e A263678 ..2....6....5....2....1....6....2....3....6....1....2....0....2....0....0....2
%e A263678 ..3....1....3....5....4....3....4....5....3....6....6....3....3....2....6....4
%e A263678 ..6....2....6....4....5....4....5....4....4....3....3....6....5....5....2....6
%e A263678 ..4....3....4....6....6....5....6....6....5....5....4....5....6....6....4....5
%Y A263678 Cf. A263683.
%K A263678 nonn
%O A263678 1,2
%A A263678 _R. H. Hardin_, Oct 23 2015