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A264017 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 1,2 or 2,2.

%I A264017 #6 Nov 10 2015 10:52:15
%S A264017 1,2,1,4,5,1,8,25,13,1,16,105,169,34,1,32,441,1573,1156,89,1,64,1869,
%T A264017 14641,20570,7921,233,1,128,7921,146410,366025,269225,54289,610,1,256,
%U A264017 33553,1464100,7320500,9150625,3524125,372100,1597,1,512,142129,14641000
%N A264017 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 1,2 or 2,2.
%C A264017 Table starts
%C A264017 .1....2........4..........8............16...............32..................64
%C A264017 .1....5.......25........105...........441.............1869................7921
%C A264017 .1...13......169.......1573.........14641...........146410.............1464100
%C A264017 .1...34.....1156......20570........366025..........7320500...........146410000
%C A264017 .1...89.....7921.....269225.......9150625........398967250.........17394972100
%C A264017 .1..233....54289....3524125.....228765625......21860843125.......2089022169025
%C A264017 .1..610...372100...46131250....5719140625....1201888840625.....252579343635025
%C A264017 .1.1597..2550409..603865625..142978515625...66099082156250...30557658560100100
%C A264017 .1.4181.17480761.7904703125.3574462890625.3635200164062500.3696969485250250000
%H A264017 R. H. Hardin, <a href="/A264017/b264017.txt">Table of n, a(n) for n = 1..143</a>
%F A264017 Empirical for column k:
%F A264017 k=1: a(n) = a(n-1)
%F A264017 k=2: a(n) = 3*a(n-1) -a(n-2)
%F A264017 k=3: a(n) = 8*a(n-1) -8*a(n-2) +a(n-3)
%F A264017 k=4: a(n) = 15*a(n-1) -25*a(n-2) for n>4
%F A264017 k=5: a(n) = 25*a(n-1) for n>3
%F A264017 k=6: a(n) = 60*a(n-1) -300*a(n-2) +1500*a(n-3) -7500*a(n-4) +3125*a(n-5) for n>7
%F A264017 k=7: [order 13] for n>15
%F A264017 Empirical for row n:
%F A264017 n=1: a(n) = 2*a(n-1)
%F A264017 n=2: a(n) = 4*a(n-1) +4*a(n-3) +a(n-4)
%F A264017 n=3: a(n) = 10*a(n-1) for n>5
%F A264017 n=4: a(n) = 19*a(n-1) +304*a(n-3) +256*a(n-4) for n>8
%F A264017 n=5: [order 14] for n>18
%F A264017 n=6: [order 25] for n>31
%e A264017 Some solutions for n=4 k=4
%e A264017 ..0..8..9..3..4....0.13..2..3..4....7..1.14..3..4....7..1.14..3..4
%e A264017 ..5.13.14..1..2...12..6..7..8..9...17..6..0..8..9...12.13..0..8..9
%e A264017 .17.18.12..6..7...22.23.24..1.14...10.11..5.13..2...17.18..5..6..2
%e A264017 .15.16.10.11.19...15.16..5.18.19...15.23.24.18.19...15.16.10.11.19
%e A264017 .20.21.22.23.24...20.21.10.11.17...20.21.22.16.12...20.21.22.23.24
%Y A264017 Column 2 is A001519(n+1).
%Y A264017 Column 3 is A081068.
%Y A264017 Row 1 is A000079(n-1).
%K A264017 nonn,tabl
%O A264017 1,2
%A A264017 _R. H. Hardin_, Nov 01 2015