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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 decreases.
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%I #4 Oct 23 2015 14:16:55

%S 1,1,2,1,2,3,1,2,5,5,1,2,5,12,8,1,2,5,17,26,13,1,2,5,17,53,58,21,1,2,

%T 5,17,70,155,131,34,1,2,5,17,70,277,429,295,55,1,2,5,17,70,349,1009,

%U 1210,662,89,1,2,5,17,70,349,1658,3487,3457,1487,144,1,2,5,17,70,349,2017

%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 decreases.

%C Table starts

%C ..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

%C ..3....5....5.....5......5......5......5......5......5......5......5......5

%C ..5...12...17....17.....17.....17.....17.....17.....17.....17.....17.....17

%C ..8...26...53....70.....70.....70.....70.....70.....70.....70.....70.....70

%C .13...58..155...277....349....349....349....349....349....349....349....349

%C .21..131..429..1009...1658...2017...2017...2017...2017...2017...2017...2017

%C .34..295.1210..3487...7356..11253..13358..13358..13358..13358..13358..13358

%C .55..662.3457.11708..30374..58743..85403..99377..99377..99377..99377..99377

%C .89.1487.9948.39905.121676.286327.514631.717372.822041.822041.822041.822041

%H R. H. Hardin, <a href="/A263683/b263683.txt">Table of n, a(n) for n = 1..484</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2)

%F k=2: a(n) = 2*a(n-1) +a(n-3) +a(n-4) -a(n-5)

%F k=3: [order 20]

%F k=4: [order 70]

%e Some solutions for n=7 k=4

%e ..2....2....0....0....0....4....1....1....1....3....0....2....2....1....0....2

%e ..0....3....4....2....1....0....5....3....2....4....5....4....1....4....4....0

%e ..3....0....3....1....4....1....2....6....0....5....1....0....5....6....5....1

%e ..4....4....6....4....3....3....3....0....4....6....2....6....0....0....1....6

%e ..5....1....1....5....5....6....0....2....6....0....3....1....4....2....6....3

%e ..1....6....2....6....6....2....4....5....3....1....4....5....6....3....2....5

%e ..6....5....5....3....2....5....6....4....5....2....6....3....3....5....3....4

%Y Column 1 is A000045(n+1).

%Y Column 2 is A116716.

%Y Diagonal is A049774.

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Oct 23 2015