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A223357 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 10
1, 4, 6, 16, 64, 36, 64, 768, 1024, 216, 256, 9216, 36864, 16384, 1296, 1024, 110592, 1327104, 1769472, 262144, 7776, 4096, 1327104, 48365568, 191102976, 84934656, 4194304, 46656, 16384, 15925248, 1764753408, 21177040896, 27518828544 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
....1.......4.........16............64..............256................1024
....6......64........768..........9216...........110592.............1327104
...36....1024......36864.......1327104.........48365568..........1764753408
..216...16384....1769472.....191102976......21177040896.......2356125106176
.1296..262144...84934656...27518828544....9273505480704....3147420753985536
.7776.4194304.4076863488.3962711310336.4060947412942848.4204783428144463872
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 6*a(n-1)
k=2: a(n) = 16*a(n-1)
k=3: a(n) = 48*a(n-1)
k=4: a(n) = 144*a(n-1)
k=5: a(n) = 480*a(n-1) -18432*a(n-2)
k=6: a(n) = 1600*a(n-1) -368640*a(n-2) +21233664*a(n-3)
k=7: a(n) = 5376*a(n-1) -5750784*a(n-2) +2038431744*a(n-3) -217432719360*a(n-4)
Empirical for row n:
n=1: a(n) = 4*a(n-1)
n=2: a(n) = 12*a(n-1) for n>2
n=3: a(n) = 40*a(n-1) -128*a(n-2) for n>4
n=4: a(n) = 144*a(n-1) -3840*a(n-2) +24576*a(n-3) for n>7
n=5: [order 7] for n>11
n=6: [order 9] for n>15
n=7: [order 27] for n>33
EXAMPLE
Some solutions for n=3 k=4
..0..2..0..2....0..3..5..2....0..2..5..4....0..4..0..4....0..1..3..4
..0..4..0..1....0..3..5..3....0..4..0..1....0..4..0..4....0..1..0..1
..0..4..5..4....0..1..0..1....0..4..2..1....0..2..0..1....0..1..2..4
CROSSREFS
Column 1 is A000400(n-1)
Column 2 is A013709 (n-1)
Column 3 is 16*48^(n-1)
Column 4 is 64*144^(n-1)
Row 1 is A000302(n-1)
Row 2 is 64*12^(n-2) for n>1
Sequence in context: A223269 A264471 A264477 * A083009 A365111 A190968
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 19 2013
STATUS
approved

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Last modified February 25 00:32 EST 2024. Contains 370308 sequences. (Running on oeis4.)