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 A263666 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. 7

%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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Last modified June 6 15:10 EDT 2023. Contains 363147 sequences. (Running on oeis4.)