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A306656 Number of ways to fill a 3D matrix with n distinct values. 0
1, 1, 6, 18, 144, 360, 6480, 15120, 403200, 2177280, 32659200, 119750400, 8622028800, 18681062400, 784604620800, 11769069312000, 313841848320000, 1067062284288000, 115242726703104000, 364935301226496000, 43792236147179520000, 459818479545384960000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
This sequence is a generalization of A323295 to the 3D case. Usually, in multidimensional data related applications (i.e., images, MRI), data is vectorized and then processed. However, because of vectorization, the spatial information in the data is lost. This reverse mapping shows the possible number of spatial states the original data could have been in.
LINKS
FORMULA
a(n) = A007425(n) * n! for n > 0, a(0) = 1.
EXAMPLE
For n = 6, a(6) = 6480, A007425(6) = 9 namely there are 9 ways to arrange 6 voxels into a 3D matrix: [1,1,6], [1,6,1], [6,1,1], [2,3,1], [3,2,1], [2,1,3], [3,1,2], [1,2,3], [1,3,2]. Then there are 6! ways to fill it with the numbers. 9*6! = 6480.
MAPLE
with(numtheory):
a:= n-> `if`(n=0, 1, add(tau(d), d=divisors(n))*n!):
seq(a(n), n=0..23); # Alois P. Heinz, Mar 03 2019
CROSSREFS
Sequence in context: A222913 A091054 A012774 * A027744 A196868 A077531
KEYWORD
nonn
AUTHOR
Yigit Oktar, Mar 03 2019
EXTENSIONS
More terms from Alois P. Heinz, Mar 03 2019
STATUS
approved

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Last modified May 26 04:31 EDT 2024. Contains 372807 sequences. (Running on oeis4.)