

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
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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!):


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



