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A263597 T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and the median of every three consecutive elements nondecreasing.

%I A263597 #4 Oct 22 2015 12:44:42
%S A263597 1,1,2,1,2,3,1,2,6,5,1,2,6,12,8,1,2,6,16,25,13,1,2,6,16,41,57,21,1,2,
%T A263597 6,16,52,108,124,34,1,2,6,16,52,164,280,268,55,1,2,6,16,52,208,476,
%U A263597 729,588,89,1,2,6,16,52,208,676,1428,1908,1285,144,1,2,6,16,52,208,800,2208,4308
%N A263597 T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and the median of every three consecutive elements nondecreasing.
%C A263597 Table starts
%C A263597 ..1....1....1.....1.....1.....1.....1.....1.....1.....1.....1.....1.....1.....1
%C A263597 ..2....2....2.....2.....2.....2.....2.....2.....2.....2.....2.....2.....2.....2
%C A263597 ..3....6....6.....6.....6.....6.....6.....6.....6.....6.....6.....6.....6.....6
%C A263597 ..5...12...16....16....16....16....16....16....16....16....16....16....16....16
%C A263597 ..8...25...41....52....52....52....52....52....52....52....52....52....52....52
%C A263597 .13...57..108...164...208...208...208...208...208...208...208...208...208...208
%C A263597 .21..124..280...476...676...800...800...800...800...800...800...800...800...800
%C A263597 .34..268..729..1428..2208..2900..3360..3360..3360..3360..3360..3360..3360..3360
%C A263597 .55..588.1908..4308..7696.10960.14024.16224.16224.16224.16224.16224.16224.16224
%C A263597 .89.1285.4969.12816.25508.40792.55492.69212.78088.78088.78088.78088.78088.78088
%H A263597 R. H. Hardin, <a href="/A263597/b263597.txt">Table of n, a(n) for n = 1..516</a>
%F A263597 Empirical for column k:
%F A263597 k=1: a(n) = a(n-1) +a(n-2)
%F A263597 k=2: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4)
%F A263597 k=3: a(n) = a(n-1) +a(n-2) +7*a(n-3) +2*a(n-4) +4*a(n-5) -a(n-7) -a(n-8)
%F A263597 k=4: [order 15]
%F A263597 k=5: [order 31]
%F A263597 k=6: [order 67]
%e A263597 Some solutions for n=6 k=4
%e A263597 ..1....1....1....0....2....0....0....0....1....4....3....2....1....4....0....2
%e A263597 ..2....2....0....1....1....5....3....1....5....1....1....0....4....0....1....0
%e A263597 ..3....3....2....3....5....2....2....2....0....0....0....1....0....1....3....1
%e A263597 ..0....0....4....4....3....3....1....5....2....2....2....5....3....3....5....3
%e A263597 ..4....5....3....2....0....4....4....3....4....3....4....3....5....2....2....4
%e A263597 ..5....4....5....5....4....1....5....4....3....5....5....4....2....5....4....5
%Y A263597 Column 1 is A000045(n+1).
%Y A263597 Column 2 is A214663.
%K A263597 nonn,tabl
%O A263597 1,3
%A A263597 _R. H. Hardin_, Oct 22 2015