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A263683 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.

%I A263683 #4 Oct 23 2015 14:16:55
%S A263683 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 A263683 5,17,70,155,131,34,1,2,5,17,70,277,429,295,55,1,2,5,17,70,349,1009,
%U A263683 1210,662,89,1,2,5,17,70,349,1658,3487,3457,1487,144,1,2,5,17,70,349,2017
%N A263683 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 A263683 Table starts
%C A263683 ..1....1....1.....1......1......1......1......1......1......1......1......1
%C A263683 ..2....2....2.....2......2......2......2......2......2......2......2......2
%C A263683 ..3....5....5.....5......5......5......5......5......5......5......5......5
%C A263683 ..5...12...17....17.....17.....17.....17.....17.....17.....17.....17.....17
%C A263683 ..8...26...53....70.....70.....70.....70.....70.....70.....70.....70.....70
%C A263683 .13...58..155...277....349....349....349....349....349....349....349....349
%C A263683 .21..131..429..1009...1658...2017...2017...2017...2017...2017...2017...2017
%C A263683 .34..295.1210..3487...7356..11253..13358..13358..13358..13358..13358..13358
%C A263683 .55..662.3457.11708..30374..58743..85403..99377..99377..99377..99377..99377
%C A263683 .89.1487.9948.39905.121676.286327.514631.717372.822041.822041.822041.822041
%H A263683 R. H. Hardin, <a href="/A263683/b263683.txt">Table of n, a(n) for n = 1..484</a>
%F A263683 Empirical for column k:
%F A263683 k=1: a(n) = a(n-1) +a(n-2)
%F A263683 k=2: a(n) = 2*a(n-1) +a(n-3) +a(n-4) -a(n-5)
%F A263683 k=3: [order 20]
%F A263683 k=4: [order 70]
%e A263683 Some solutions for n=7 k=4
%e A263683 ..2....2....0....0....0....4....1....1....1....3....0....2....2....1....0....2
%e A263683 ..0....3....4....2....1....0....5....3....2....4....5....4....1....4....4....0
%e A263683 ..3....0....3....1....4....1....2....6....0....5....1....0....5....6....5....1
%e A263683 ..4....4....6....4....3....3....3....0....4....6....2....6....0....0....1....6
%e A263683 ..5....1....1....5....5....6....0....2....6....0....3....1....4....2....6....3
%e A263683 ..1....6....2....6....6....2....4....5....3....1....4....5....6....3....2....5
%e A263683 ..6....5....5....3....2....5....6....4....5....2....6....3....3....5....3....4
%Y A263683 Column 1 is A000045(n+1).
%Y A263683 Column 2 is A116716.
%Y A263683 Diagonal is A049774.
%K A263683 nonn,tabl
%O A263683 1,3
%A A263683 _R. H. Hardin_, Oct 23 2015