OFFSET
1,2
COMMENTS
a(n) is the volume (or the number of cubes) in a polycube whose base is the symmetric representation of A024916(n) which is formed with the first n 3D-Ziggurats described in A347186.
a(n) is also the total number of cubes in a three-dimensional spiral formed with the first n 3D-Ziggurats described in A347186 (see example). The base of the 3D-spiral is the spiral formed with the symmetric representation of sigma of the first n positive integers as shown in the example section of A239660.
EXAMPLE
For n = 16 the figure shows the top view of a three-dimensional spiral formed with the first 16 3D-Ziggurats described in A347186. There are four 3D-Ziggurats in every quadrant:
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|_| |_| |_| |_| |_| |_| |_| |_|
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The number of square cells in the top view of the n-th 3D-Ziggurat equals A000203(n).
The total number of square cells in the top view of the 3D-Spiral with the first n 3D-Ziggurats equals A024916(n).
In the above figure the total number of square cells equals A024916(16) = 220.
a(16) = 1064 is the total number of cubes in the 3D-Spiral with the first 16 3D-Ziggurats.
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Oct 15 2022
STATUS
approved