A263714 - OEIS

%I #4 Oct 24 2015 11:44:53

%S 1,1,2,1,2,3,1,2,6,5,1,2,6,14,8,1,2,6,24,31,11,1,2,6,24,78,34,17,1,2,

%T 6,24,120,60,39,25,1,2,6,24,120,72,50,46,37,1,2,6,24,120,144,54,52,64,

%U 57,1,2,6,24,120,144,60,54,70,104,84,1,2,6,24,120,144,108,54,72,116,161,127,1

%N 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 four consecutive elements having its maximum within 4 of its minimum

%C Table starts

%C ...1...1...1...1...1...1...1...1...1...1...1...1...1...1...1...1...1...1...1

%C ...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2

%C ...3...6...6...6...6...6...6...6...6...6...6...6...6...6...6...6...6...6...6

%C ...5..14..24..24..24..24..24..24..24..24..24..24..24..24..24..24..24..24..24

%C ...8..31..78.120.120.120.120.120.120.120.120.120.120.120.120.120.120.120.120

%C ..11..34..60..72.144.144.144.144.144.144.144.144.144.144.144.144.144.144.144

%C ..17..39..50..54..60.108.108.108.108.108.108.108.108.108.108.108.108.108.108

%C ..25..46..52..54..54..60.108.108.108.108.108.108.108.108.108.108.108.108.108

%C ..37..64..70..72..72..72..81.144.144.144.144.144.144.144.144.144.144.144.144

%C ..57.104.116.120.120.120.120.147.240.240.240.240.240.240.240.240.240.240.240

%C ..84.161.184.192.192.192.192.192.228.384.384.384.384.384.384.384.384.384.384

%C .127.249.292.308.308.308.308.308.308.368.616.616.616.616.616.616.616.616.616

%C .191.385.449.480.480.480.480.480.480.480.576.960.960.960.960.960.960.960.960

%H R. H. Hardin, <a href="/A263714/b263714.txt">Table of n, a(n) for n = 1..618</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-3) -a(n-4) +2*a(n-5) -a(n-6) +a(n-7)

%F k=2: a(n) = a(n-1) +a(n-3) -a(n-4) +2*a(n-5) -a(n-6) +a(n-7) for n>18

%F k=3: a(n) = a(n-1) +a(n-3) -a(n-4) +2*a(n-5) -a(n-6) +a(n-7) for n>18

%F k=4: a(n) = a(n-1) +a(n-3) -a(n-4) +2*a(n-5) -a(n-6) +a(n-7) for n>18

%F k=5: a(n) = a(n-1) +a(n-3) -a(n-4) +2*a(n-5) -a(n-6) +a(n-7) for n>18

%F k=6: a(n) = a(n-1) +a(n-3) -a(n-4) +2*a(n-5) -a(n-6) +a(n-7) for n>18

%F k=7: a(n) = a(n-1) +a(n-3) -a(n-4) +2*a(n-5) -a(n-6) +a(n-7) for n>18

%e Some solutions for n=7 k=4

%e ..0....0....1....0....0....0....0....3....1....0....0....0....0....1....1....0

%e ..1....1....0....1....4....1....1....0....0....1....2....1....1....0....0....1

%e ..3....3....3....2....1....3....2....1....3....3....1....2....3....4....4....4

%e ..4....2....4....3....3....4....4....4....2....2....4....3....2....2....3....2

%e ..2....5....2....5....5....5....5....2....4....4....3....4....4....3....2....3

%e ..5....4....5....6....2....6....3....5....5....5....5....5....6....5....5....5

%e ..6....6....6....4....6....2....6....6....6....6....6....6....5....6....6....6

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Oct 24 2015