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A264172 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

%I A264172 #6 Nov 10 2015 11:46:51
%S A264172 1,4,4,8,25,8,16,98,98,16,33,418,733,418,33,69,1862,6017,6017,1862,69,
%T A264172 145,8007,50237,96296,50237,8007,145,300,34539,408698,1531900,1531900,
%U A264172 408698,34539,300,624,149808,3328825,23916656,47277776,23916656,3328825
%N A264172 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.
%C A264172 Table starts
%C A264172 ....1.......4..........8............16...............33................69
%C A264172 ....4......25.........98...........418.............1862..............8007
%C A264172 ....8......98........733..........6017............50237............408698
%C A264172 ...16.....418.......6017.........96296..........1531900..........23916656
%C A264172 ...33....1862......50237.......1531900.........47277776........1432853288
%C A264172 ...69....8007.....408698......23916656.......1432853288.......83609564805
%C A264172 ..145...34539....3328825.....375202191......43416669841.....4868342507373
%C A264172 ..300..149808...27209977....5888212022....1312690666360...283367589816531
%C A264172 ..624..648436..222177128...92168640612...39639424508160.16469467179397573
%C A264172 .1300.2805250.1813435208.1442827111989.1196969465424056
%H A264172 R. H. Hardin, <a href="/A264172/b264172.txt">Table of n, a(n) for n = 1..111</a>
%F A264172 Empirical for column k:
%F A264172 k=1: a(n) = a(n-1) +a(n-2) +2*a(n-3) +a(n-4) +a(n-5) -a(n-6)
%F A264172 k=2: a(n) = a(n-1) +7*a(n-2) +23*a(n-3) +35*a(n-4) +18*a(n-5) for n>7
%F A264172 k=3: [order 56]
%e A264172 Some solutions for n=4 k=4
%e A264172 ..7..1..2..3..4....0..8..1..2..3....0..1..2.14..3....0..1.13..2..3
%e A264172 ..0.13..6.19..9....5.13.14..7..4...12..5..6..7..4....5..6..7..8..4
%e A264172 ..5.10.11..8.14...10..6.12.24..9...10.22.11..8..9...17.10.19.12..9
%e A264172 .22.16.12.17.18...15.11.17.18.19...15.23.17.13.19...15.11.16.18.14
%e A264172 .15.20.21.23.24...20.16.21.22.23...20.16.21.18.24...20.21.22.23.24
%K A264172 nonn,tabl
%O A264172 1,2
%A A264172 _R. H. Hardin_, Nov 06 2015