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A186410
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Number of "ON" cells at n-th stage of three-dimensional version of the cellular automaton A183060 using cubes.
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3
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0, 1, 6, 11, 32, 37, 58, 79, 180, 185, 206, 227, 328, 349, 450, 551, 1052, 1057, 1078, 1099, 1200, 1221, 1322, 1423, 1924, 1945, 2046, 2147, 2648, 2749, 3250, 3751, 6252, 6257, 6278, 6299, 6400, 6421, 6522, 6623
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OFFSET
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0,3
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COMMENTS
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The sequence gives the total number of cells turned ON after n stages in a cellular automaton based on Z^3 lattice in the same way that A183060 is based on the Z^2 lattice. In general here each cell has six neighbors.
It appears that after 2^k stages the structure resembles a pyramid. For the first differences see A186411.
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LINKS
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FORMULA
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a(n) = n + (4/5)*(Sum_{i=1..n-1} 5^A000120(i)).
a(2^n) = 2^n + (4/5)*(6^n - 1).
(End)
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MATHEMATICA
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a[n_] := n + (4/5) Sum[5^DigitCount[i, 2, 1], {i, n - 1}]; Array[a, 40, 0] (* Michael De Vlieger, Nov 02 2022 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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