A223357 - OEIS

%I #4 Mar 19 2013 13:50:23

%S 1,4,6,16,64,36,64,768,1024,216,256,9216,36864,16384,1296,1024,110592,

%T 1327104,1769472,262144,7776,4096,1327104,48365568,191102976,84934656,

%U 4194304,46656,16384,15925248,1764753408,21177040896,27518828544

%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 or antidiagonal neighbor moves across a corresponding cube edge

%C Table starts

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

%C ....6......64........768..........9216...........110592.............1327104

%C ...36....1024......36864.......1327104.........48365568..........1764753408

%C ..216...16384....1769472.....191102976......21177040896.......2356125106176

%C .1296..262144...84934656...27518828544....9273505480704....3147420753985536

%C .7776.4194304.4076863488.3962711310336.4060947412942848.4204783428144463872

%H R. H. Hardin, <a href="/A223357/b223357.txt">Table of n, a(n) for n = 1..241</a>

%F Empirical for column k:

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

%F k=2: a(n) = 16*a(n-1)

%F k=3: a(n) = 48*a(n-1)

%F k=4: a(n) = 144*a(n-1)

%F k=5: a(n) = 480*a(n-1) -18432*a(n-2)

%F k=6: a(n) = 1600*a(n-1) -368640*a(n-2) +21233664*a(n-3)

%F k=7: a(n) = 5376*a(n-1) -5750784*a(n-2) +2038431744*a(n-3) -217432719360*a(n-4)

%F Empirical for row n:

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

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

%F n=3: a(n) = 40*a(n-1) -128*a(n-2) for n>4

%F n=4: a(n) = 144*a(n-1) -3840*a(n-2) +24576*a(n-3) for n>7

%F n=5: [order 7] for n>11

%F n=6: [order 9] for n>15

%F n=7: [order 27] for n>33

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A000400(n-1)

%Y Column 2 is A013709 (n-1)

%Y Column 3 is 16*48^(n-1)

%Y Column 4 is 64*144^(n-1)

%Y Row 1 is A000302(n-1)

%Y Row 2 is 64*12^(n-2) for n>1

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Mar 19 2013