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A263643 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.

%I A263643 #4 Oct 22 2015 14:48:29
%S A263643 1,1,2,1,2,2,1,2,5,2,1,2,5,9,2,1,2,5,17,11,2,1,2,5,17,41,19,2,1,2,5,
%T A263643 17,70,75,27,2,1,2,5,17,70,226,156,44,2,1,2,5,17,70,349,538,340,65,2,
%U A263643 1,2,5,17,70,349,1389,1417,738,104,2,1,2,5,17,70,349,2017,4255,3734,1567,155,2
%N A263643 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.
%C A263643 Table starts
%C A263643 .1...1....1.....1.....1......1......1......1......1......1......1......1......1
%C A263643 .2...2....2.....2.....2......2......2......2......2......2......2......2......2
%C A263643 .2...5....5.....5.....5......5......5......5......5......5......5......5......5
%C A263643 .2...9...17....17....17.....17.....17.....17.....17.....17.....17.....17.....17
%C A263643 .2..11...41....70....70.....70.....70.....70.....70.....70.....70.....70.....70
%C A263643 .2..19...75...226...349....349....349....349....349....349....349....349....349
%C A263643 .2..27..156...538..1389...2017...2017...2017...2017...2017...2017...2017...2017
%C A263643 .2..44..340..1417..4255...9673..13358..13358..13358..13358..13358..13358..13358
%C A263643 .2..65..738..3734.13529..36321..74678..99377..99377..99377..99377..99377..99377
%C A263643 .2.104.1567.10564.42700.138420.335720.636645.822041.822041.822041.822041.822041
%H A263643 R. H. Hardin, <a href="/A263643/b263643.txt">Table of n, a(n) for n = 1..484</a>
%F A263643 Empirical for column k:
%F A263643 k=2: a(n) = 2*a(n-2) +a(n-3) -a(n-5) for n>9
%F A263643 k=3: [order 14] for n>19
%F A263643 k=4: [order 46] for n>53
%e A263643 Some solutions for n=6 k=4
%e A263643 ..2....2....3....0....2....3....3....4....1....4....1....4....4....0....4....1
%e A263643 ..0....1....0....5....5....1....4....0....4....5....5....2....3....5....1....0
%e A263643 ..4....4....2....1....3....5....2....2....0....2....4....5....5....2....0....4
%e A263643 ..1....0....1....3....0....0....5....1....3....0....0....3....0....3....5....3
%e A263643 ..5....5....5....2....4....4....0....5....2....3....3....0....2....1....2....5
%e A263643 ..3....3....4....4....1....2....1....3....5....1....2....1....1....4....3....2
%Y A263643 Diagonal is A049774.
%K A263643 nonn,tabl
%O A263643 1,3
%A A263643 _R. H. Hardin_, Oct 22 2015