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A263703 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 4 of its minimum.

%I A263703 #4 Oct 24 2015 06:48:21
%S A263703 1,1,2,1,2,3,1,2,6,5,1,2,6,14,8,1,2,6,24,31,13,1,2,6,24,78,56,21,1,2,
%T A263703 6,24,120,110,104,34,1,2,6,24,120,168,169,208,55,1,2,6,24,120,288,204,
%U A263703 301,418,89,1,2,6,24,120,288,276,348,616,873,144,1,2,6,24,120,288,456,374
%N A263703 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 4 of its minimum.
%C A263703 Table starts
%C A263703 ...1....1.....1.....1.....1.....1.....1.....1.....1.....1.....1.....1.....1
%C A263703 ...2....2.....2.....2.....2.....2.....2.....2.....2.....2.....2.....2.....2
%C A263703 ...3....6.....6.....6.....6.....6.....6.....6.....6.....6.....6.....6.....6
%C A263703 ...5...14....24....24....24....24....24....24....24....24....24....24....24
%C A263703 ...8...31....78...120...120...120...120...120...120...120...120...120...120
%C A263703 ..13...56...110...168...288...288...288...288...288...288...288...288...288
%C A263703 ..21..104...169...204...276...456...456...456...456...456...456...456...456
%C A263703 ..34..208...301...348...374...488...768...768...768...768...768...768...768
%C A263703 ..55..418...616...696...732...754..1002..1508..1508..1508..1508..1508..1508
%C A263703 ..89..873..1373..1601..1673..1699..1759..2393..3434..3434..3434..3434..3434
%C A263703 .144.1772..2908..3476..3692..3744..3766..3906..5238..7560..7560..7560..7560
%C A263703 .233.3545..5908..7244..7784..7940..7984..7999..8312.11107.16024.16024.16024
%C A263703 .377.7103.11544.14048.15360.15748.15880.15908.15930.16548.21922.31872.31872
%H A263703 R. H. Hardin, <a href="/A263703/b263703.txt">Table of n, a(n) for n = 1..653</a>
%F A263703 Empirical for column k:
%F A263703 k=1: a(n) = a(n-1) +a(n-2)
%F A263703 k=2: a(n) = a(n-1) +a(n-2) +7*a(n-5) +2*a(n-6) +a(n-7) +5*a(n-8) -4*a(n-9) -3*a(n-10) -3*a(n-11) -4*a(n-12) -4*a(n-14) -a(n-15) +3*a(n-16) -a(n-17) +a(n-19)
%F A263703 k=3: [same order 19] for n>27
%F A263703 k=4: [same order 19] for n>27
%F A263703 k=5: [same order 19] for n>29
%F A263703 k=6: [same order 19] for n>31
%F A263703 k=7: [same order 19] for n>33
%e A263703 Some solutions for n=7 k=4
%e A263703 ..1....1....4....0....0....3....1....0....4....0....0....0....2....1....1....0
%e A263703 ..3....0....2....3....1....1....0....1....0....1....2....3....0....0....4....1
%e A263703 ..0....2....0....1....4....0....2....2....1....4....1....1....4....4....0....3
%e A263703 ..4....4....1....5....5....4....4....3....2....3....5....2....1....2....2....2
%e A263703 ..2....6....3....2....3....2....3....6....5....6....4....5....3....5....3....6
%e A263703 ..5....5....5....6....2....6....6....4....6....2....3....6....5....6....5....4
%e A263703 ..6....3....6....4....6....5....5....5....3....5....6....4....6....3....6....5
%Y A263703 Column 1 is A000045(n+1).
%K A263703 nonn,tabl
%O A263703 1,3
%A A263703 _R. H. Hardin_, Oct 24 2015