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A263693 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 3 of its minimum.

%I A263693 #4 Oct 23 2015 20:46:34
%S A263693 1,1,2,1,2,3,1,2,6,5,1,2,6,14,7,1,2,6,24,14,11,1,2,6,24,18,16,16,1,2,
%T A263693 6,24,36,18,22,25,1,2,6,24,36,20,24,36,37,1,2,6,24,36,36,24,40,56,57,
%U A263693 1,2,6,24,36,36,27,40,64,85,85,1,2,6,24,36,36,48,40,64,100,125,130,1,2,6,24,36
%N A263693 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 3 of its minimum.
%C A263693 Table starts
%C A263693 ...1...1...1...1...1...1...1...1...1...1...1...1...1...1...1...1...1...1...1
%C A263693 ...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2
%C A263693 ...3...6...6...6...6...6...6...6...6...6...6...6...6...6...6...6...6...6...6
%C A263693 ...5..14..24..24..24..24..24..24..24..24..24..24..24..24..24..24..24..24..24
%C A263693 ...7..14..18..36..36..36..36..36..36..36..36..36..36..36..36..36..36..36..36
%C A263693 ..11..16..18..20..36..36..36..36..36..36..36..36..36..36..36..36..36..36..36
%C A263693 ..16..22..24..24..27..48..48..48..48..48..48..48..48..48..48..48..48..48..48
%C A263693 ..25..36..40..40..40..49..80..80..80..80..80..80..80..80..80..80..80..80..80
%C A263693 ..37..56..64..64..64..64..76.128.128.128.128.128.128.128.128.128.128.128.128
%C A263693 ..57..85.100.100.100.100.100.120.200.200.200.200.200.200.200.200.200.200.200
%C A263693 ..85.125.144.144.144.144.144.144.168.288.288.288.288.288.288.288.288.288.288
%C A263693 .130.189.216.216.216.216.216.216.216.256.432.432.432.432.432.432.432.432.432
%C A263693 .195.285.324.324.324.324.324.324.324.324.380.648.648.648.648.648.648.648.648
%H A263693 R. H. Hardin, <a href="/A263693/b263693.txt">Table of n, a(n) for n = 1..653</a>
%F A263693 Empirical for diagonal: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>12
%F A263693 Empirical for column k:
%F A263693 k=1: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4)
%F A263693 k=2: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>12
%F A263693 k=3: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>12
%F A263693 k=4: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>12
%F A263693 k=5: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>12
%F A263693 k=6: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>12
%F A263693 k=7: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>13
%e A263693 Some solutions for n=7 k=4
%e A263693 ..1....0....0....3....1....0....0....0....0....0....0....0....1....0....1....2
%e A263693 ..0....2....1....0....0....1....1....1....1....2....1....2....0....1....0....0
%e A263693 ..2....1....2....1....3....2....2....2....2....1....2....1....2....2....3....1
%e A263693 ..3....3....3....2....2....4....3....4....3....3....4....4....3....4....2....3
%e A263693 ..4....4....4....4....4....3....5....5....4....4....3....3....5....5....5....4
%e A263693 ..6....5....6....5....5....6....4....6....5....6....5....6....6....3....4....6
%e A263693 ..5....6....5....6....6....5....6....3....6....5....6....5....4....6....6....5
%Y A263693 Column 1 is A130137(n-1).
%K A263693 nonn,tabl
%O A263693 1,3
%A A263693 _R. H. Hardin_, Oct 23 2015