A223269 - OEIS

%I #4 Mar 19 2013 07:25:52

%S 1,4,6,16,48,36,64,576,576,216,256,6144,20992,6912,1296,1024,67584,

%T 622592,765952,82944,7776,4096,737280,19726336,63438848,27951104,

%U 995328,46656,16384,8060928,611319808,5889851392,6467616768,1020002304,11943936

%N T(n,k)=Rolling cube face footprints: number of nXk 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge

%C Table starts

%C ....1......4.........16...........64.............256...............1024

%C ....6.....48........576.........6144...........67584.............737280

%C ...36....576......20992.......622592........19726336..........611319808

%C ..216...6912.....765952.....63438848......5889851392.......522106961920

%C .1296..82944...27951104...6467616768...1771674009600....450204914417664

%C .7776.995328.1020002304.659411697664.534392715870208.389343801904201728

%H R. H. Hardin, <a href="/A223269/b223269.txt">Table of n, a(n) for n = 1..311</a>

%F Empirical for column k:

%F k=1: a(n) = 6*a(n-1)

%F k=2: a(n) = 12*a(n-1)

%F k=3: a(n) = 40*a(n-1) -128*a(n-2)

%F k=4: a(n) = 112*a(n-1) -1024*a(n-2)

%F k=5: [order 6]

%F k=6: [order 9]

%F k=7: [order 19]

%F Empirical for row n:

%F n=1: a(n) = 4*a(n-1)

%F n=2: a(n) = 8*a(n-1) +32*a(n-2)

%F n=3: a(n) = 24*a(n-1) +256*a(n-2) -1024*a(n-3) for n>4

%F n=4: [order 6] for n>7

%F n=5: [order 10] for n>11

%F n=6: [order 23] for n>24

%e Some solutions for n=3 k=4

%e ..0..3..1..2....0..1..0..1....0..4..5..1....0..4..2..4....0..2..1..3

%e ..0..2..4..3....0..3..5..1....0..4..0..3....0..1..0..4....0..3..4..2

%e ..4..2..1..2....0..2..0..1....3..1..5..4....3..4..0..1....0..3..4..0

%e Face neighbors:

%e 0.->.1.2.3.4

%e 1.->.0.2.3.5

%e 2.->.0.1.4.5

%e 3.->.0.1.4.5

%e 4.->.0.3.2.5

%e 5.->.1.3.4.2

%Y Column 1 is A000400(n-1)

%Y Column 2 is 4*12^(n-1)

%Y Column 3 is A223197

%Y Row 1 is A000302(n-1)

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Mar 19 2013