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%I #4 Oct 23 2015 11:22:59
%S 1,1,2,1,2,2,1,2,4,2,1,2,4,7,2,1,2,4,10,8,2,1,2,4,10,22,12,2,1,2,4,10,
%T 32,40,16,2,1,2,4,10,32,95,70,24,2,1,2,4,10,32,122,208,133,32,2,1,2,4,
%U 10,32,122,422,486,254,48,2,1,2,4,10,32,122,544,1222,1064,482,64,2,1,2,4,10,32
%N T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and with no two consecutive increases or two consecutive decreases.
%C Table starts
%C .1..1...1....1....1.....1.....1.....1......1......1......1......1......1......1
%C .2..2...2....2....2.....2.....2.....2......2......2......2......2......2......2
%C .2..4...4....4....4.....4.....4.....4......4......4......4......4......4......4
%C .2..7..10...10...10....10....10....10.....10.....10.....10.....10.....10.....10
%C .2..8..22...32...32....32....32....32.....32.....32.....32.....32.....32.....32
%C .2.12..40...95..122...122...122...122....122....122....122....122....122....122
%C .2.16..70..208..422...544...544...544....544....544....544....544....544....544
%C .2.24.133..486.1222..2287..2770..2770...2770...2770...2770...2770...2770...2770
%C .2.32.254.1064.3302..7688.13102.15872..15872..15872..15872..15872..15872..15872
%C .2.48.482.2560.9021.25662.53324.86555.101042.101042.101042.101042.101042.101042
%H R. H. Hardin, <a href="/A263666/b263666.txt">Table of n, a(n) for n = 1..484</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) for n>2
%F k=2: a(n) = 2*a(n-2) for n>6
%F k=3: a(n) = 3*a(n-2) +2*a(n-4) for n>12
%F k=4: a(n) = 4*a(n-2) +6*a(n-4) +16*a(n-6) -8*a(n-10) for n>20
%F k=5: [order 22] for n>34
%F k=6: [order 52] for n>66
%e Some solutions for n=7 k=4
%e ..1....1....1....0....1....2....2....2....4....3....1....1....3....4....1....4
%e ..0....0....5....3....5....1....0....3....0....1....5....0....4....0....4....0
%e ..6....6....3....1....4....5....6....0....6....4....0....5....1....3....2....5
%e ..4....2....4....5....6....0....1....6....2....0....6....4....6....2....6....1
%e ..5....5....0....2....0....6....4....1....5....6....3....6....0....5....0....6
%e ..2....3....6....6....3....3....3....5....1....2....4....2....5....1....5....2
%e ..3....4....2....4....2....4....5....4....3....5....2....3....2....6....3....3
%Y Diagonal is A001250.
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_, Oct 23 2015
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