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A356351
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Partial sums of the ziggurat sequence A347186.
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1
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1, 5, 11, 27, 39, 76, 96, 160, 196, 286, 328, 489, 545, 701, 808, 1064, 1154, 1488, 1598, 2006, 2208, 2550, 2706, 3403, 3610, 4072, 4384, 5169, 5409, 6385, 6657, 7681, 8127, 8883, 9324, 10910, 11290, 12220, 12824, 14560, 15022, 16863, 17369, 19175, 20276, 21608, 22208, 25129, 25849, 27669
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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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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.
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CROSSREFS
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Cf. A000203, A024916, A196020, A235791, A236104, A237270, A237591, A237593, A239660, A239931, A239932, A239933, A239934, A347186, A296508, A299778, A347186, A347263, A347367, A347529, A351819.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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