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A264142 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 1,1.

%I A264142 #6 Nov 10 2015 11:16:35
%S A264142 2,8,4,18,27,8,45,144,125,16,125,720,1440,512,32,320,3600,15488,14400,
%T A264142 2197,64,832,18000,168948,297920,144000,9261,128,2197,90000,1903336,
%U A264142 7001316,5953600,1440000,39304,256,5733,450000,20768650,163887724
%N A264142 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 1,1.
%C A264142 Table starts
%C A264142 ...2.....8.......18.........45..........125.............320...............832
%C A264142 ...4....27......144........720.........3600...........18000.............90000
%C A264142 ...8...125.....1440......15488.......168948.........1903336..........20768650
%C A264142 ..16...512....14400.....297920......7001316.......163887724........3798503424
%C A264142 ..32..2197...144000....5953600....302693857.....15238898080......758116015189
%C A264142 ..64..9261..1440000..117534144..12968882161...1376159333484...147813083354689
%C A264142 .128.39304.14400000.2330885440.557669432592.125699825697364.29086230347332416
%H A264142 R. H. Hardin, <a href="/A264142/b264142.txt">Table of n, a(n) for n = 1..97</a>
%F A264142 Empirical for column k:
%F A264142 k=1: a(n) = 2*a(n-1)
%F A264142 k=2: a(n) = 3*a(n-1) +6*a(n-2) -3*a(n-3) -a(n-4)
%F A264142 k=3: a(n) = 10*a(n-1) for n>2
%F A264142 k=4: [order 8]
%F A264142 k=5: [order 32]
%F A264142 k=6: [order 95]
%F A264142 Empirical for row n:
%F A264142 n=1: a(n) = 3*a(n-1) -a(n-2) +3*a(n-3) -9*a(n-4) +3*a(n-5) -a(n-6) +3*a(n-7) -a(n-8)
%F A264142 n=2: a(n) = 5*a(n-1) for n>3
%F A264142 n=3: [order 67]
%F A264142 n=4: [order 95]
%e A264142 Some solutions for n=3 k=4
%e A264142 ..0..1..2..6..4....6..1..2..3..4....6..1..8..9..4....6..7..5..9..4
%e A264142 ..5..3..7.11.12...11..0.10..8..9....2..0..7.11..3....2..0..1..8..3
%e A264142 .10.17..9.16..8....7..5.12.13.17...10..5.12.16.17...10.11.15.13.17
%e A264142 .15.13.14.18.19...15.16.14.18.19...15.13.14.18.19...12.16.14.18.19
%Y A264142 Column 1 is A000079.
%Y A264142 Column 2 is A056570(n+2).
%Y A264142 Row 1 is A264054.
%K A264142 nonn,tabl
%O A264142 1,1
%A A264142 _R. H. Hardin_, Nov 04 2015