A264172 - OEIS

%I #6 Nov 10 2015 11:46:51

%S 1,4,4,8,25,8,16,98,98,16,33,418,733,418,33,69,1862,6017,6017,1862,69,

%T 145,8007,50237,96296,50237,8007,145,300,34539,408698,1531900,1531900,

%U 408698,34539,300,624,149808,3328825,23916656,47277776,23916656,3328825

%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 directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.

%C Table starts

%C ....1.......4..........8............16...............33................69

%C ....4......25.........98...........418.............1862..............8007

%C ....8......98........733..........6017............50237............408698

%C ...16.....418.......6017.........96296..........1531900..........23916656

%C ...33....1862......50237.......1531900.........47277776........1432853288

%C ...69....8007.....408698......23916656.......1432853288.......83609564805

%C ..145...34539....3328825.....375202191......43416669841.....4868342507373

%C ..300..149808...27209977....5888212022....1312690666360...283367589816531

%C ..624..648436..222177128...92168640612...39639424508160.16469467179397573

%C .1300.2805250.1813435208.1442827111989.1196969465424056

%H R. H. Hardin, <a href="/A264172/b264172.txt">Table of n, a(n) for n = 1..111</a>

%F Empirical for column k:

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

%F 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 k=3: [order 56]

%e Some solutions for n=4 k=4

%e ..7..1..2..3..4....0..8..1..2..3....0..1..2.14..3....0..1.13..2..3

%e ..0.13..6.19..9....5.13.14..7..4...12..5..6..7..4....5..6..7..8..4

%e ..5.10.11..8.14...10..6.12.24..9...10.22.11..8..9...17.10.19.12..9

%e .22.16.12.17.18...15.11.17.18.19...15.23.17.13.19...15.11.16.18.14

%e .15.20.21.23.24...20.16.21.22.23...20.16.21.18.24...20.21.22.23.24

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 06 2015