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A263752 T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and every three consecutive elements having its maximum within 5 of its minimum.

%I A263752 #6 Jul 23 2025 15:37:27
%S A263752 1,1,2,1,2,3,1,2,6,5,1,2,6,14,8,1,2,6,24,31,13,1,2,6,24,78,73,21,1,2,
%T A263752 6,24,120,230,160,34,1,2,6,24,120,504,506,357,55,1,2,6,24,120,720,930,
%U A263752 1128,814,89,1,2,6,24,120,720,1560,1794,2641,1836,144,1,2,6,24,120,720,2400
%N A263752 T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and every three consecutive elements having its maximum within 5 of its minimum.
%C A263752 Table starts
%C A263752 ..1....1....1....1.....1.....1.....1.....1.....1.....1.....1.....1.....1.....1
%C A263752 ..2....2....2....2.....2.....2.....2.....2.....2.....2.....2.....2.....2.....2
%C A263752 ..3....6....6....6.....6.....6.....6.....6.....6.....6.....6.....6.....6.....6
%C A263752 ..5...14...24...24....24....24....24....24....24....24....24....24....24....24
%C A263752 ..8...31...78..120...120...120...120...120...120...120...120...120...120...120
%C A263752 .13...73..230..504...720...720...720...720...720...720...720...720...720...720
%C A263752 .21..160..506..930..1560..2400..2400..2400..2400..2400..2400..2400..2400..2400
%C A263752 .34..357.1128.1794..2352..3552..5424..5424..5424..5424..5424..5424..5424..5424
%C A263752 .55..814.2641.3852..4704..5484..7872.11568.11568.11568.11568.11568.11568.11568
%C A263752 .89.1836.6655.9246.10946.12058.13426.18918.26796.26796.26796.26796.26796.26796
%H A263752 R. H. Hardin, <a href="/A263752/b263752.txt">Table of n, a(n) for n = 1..652</a>
%F A263752 Empirical for column k:
%F A263752 k=1: a(n) = a(n-1) +a(n-2)
%F A263752 k=2: [order 13]
%F A263752 k=3: [order 62]
%F A263752 k=4: [same order 62] for n>74
%F A263752 k=5: [same order 62] for n>74
%F A263752 k=6: [same order 62] for n>76
%F A263752 k=7: [same order 62] for n>78
%e A263752 Some solutions for n=10 k=4
%e A263752 ..0....4....1....0....1....0....0....0....0....4....1....3....1....2....0....0
%e A263752 ..1....1....3....2....0....3....2....5....1....0....3....5....3....0....5....1
%e A263752 ..2....0....2....1....2....2....1....1....3....2....2....4....0....1....1....3
%e A263752 ..3....3....0....3....4....1....3....6....2....1....0....0....2....4....2....2
%e A263752 ..5....2....4....4....3....4....4....2....4....3....4....1....4....5....3....7
%e A263752 ..8....5....5....7....5....6....5....3....7....5....5....2....7....3....7....5
%e A263752 ..4....6....6....9....6....7....8....4....9....6....8....6....8....6....4....4
%e A263752 ..9....7....9....6....7....8....7....7....6....9....7....7....6....7....8....6
%e A263752 ..6....8....7....5....9....5....9....8....5....7....6....8....5....9....6....9
%e A263752 ..7....9....8....8....8....9....6....9....8....8....9....9....9....8....9....8
%Y A263752 Column 1 is A000045(n+1)
%K A263752 nonn,tabl
%O A263752 1,3
%A A263752 _R. H. Hardin_, Oct 25 2015