A264131 - OEIS

%I #6 Nov 10 2015 11:05:11

%S 1,5,1,25,13,1,80,169,34,1,256,1040,1156,89,1,976,6400,13600,7921,233,

%T 1,3721,53280,160000,178000,54289,610,1,13725,443556,2920000,4000000,

%U 2330000,372100,1597,1,50625,3383280,53290000,160564000,100000000

%N T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having index change +-(.,.) 0,0 0,2 or 1,2.

%C Table starts

%C .1.....5........25.........80.........256..........976.........3721

%C .1....13.......169.......1040........6400........53280.......443556

%C .1....34......1156......13600......160000......2920000.....53290000

%C .1....89......7921.....178000.....4000000....160564000...6445199524

%C .1...233.....54289....2330000...100000000...8830490000.779775536401

%C .1...610....372100...30500000..2500000000.485643650000

%C .1..1597...2550409..399250000.62500000000

%C .1..4181..17480761.5226250000

%C .1.10946.119814916

%C .1.28657

%H R. H. Hardin, <a href="/A264131/b264131.txt">Table of n, a(n) for n = 1..71</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

%F k=2: a(n) = 3*a(n-1) -a(n-2)

%F k=3: a(n) = 8*a(n-1) -8*a(n-2) +a(n-3)

%F k=4: a(n) = 15*a(n-1) -25*a(n-2)

%F k=5: a(n) = 25*a(n-1)

%F k=6: a(n) = 60*a(n-1) -300*a(n-2) +1500*a(n-3) -7500*a(n-4) +3125*a(n-5)

%F Empirical for row n:

%F n=1: a(n) = 4*a(n-1) -a(n-2) +15*a(n-4) -60*a(n-5) +15*a(n-6) -15*a(n-8) +60*a(n-9) -15*a(n-10) +a(n-12) -4*a(n-13) +a(n-14)

%e Some solutions for n=4 k=4

%e ..0..1..9..3..4....0..1..4..3..2....0..1..2..3..4....0..1..4..3..2

%e ..7..8..5..6..2....5..8.14..6..9....5..8..7..6..9....7..8..5..6..9

%e .10.11.14.13.12...12.18.10.13..7...17.18.19.13.14...10.13.19.11.14

%e .15.16.24.18.19...15.16.19.11.17...15.23.10.11.12...22.18.15.16.12

%e .22.21.20.23.17...20.21.24.23.22...20.21.22.16.24...20.23.24.21.17

%Y Column 2 is A001519(n+2).

%Y Column 3 is A081068(n+1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 03 2015