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A161342
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Number of "ON" cubic cells at n-th stage in simple 3-dimensional cellular automaton: a(n) = A160428(n)/8.
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9
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0, 1, 8, 15, 64, 71, 120, 169, 512, 519, 568, 617, 960, 1009, 1352, 1695, 4096, 4103, 4152, 4201, 4544, 4593, 4936, 5279, 7680, 7729, 8072, 8415, 10816, 11159, 13560, 15961, 32768, 32775, 32824, 32873, 33216, 33265, 33608, 33951, 36352, 36401, 36744, 37087, 39488
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OFFSET
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0,3
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COMMENTS
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Let M =
1, 0, 0, 0, 0, ...
8, 0, 0, 0, 0, ...
7, 1, 0, 0, 0, ...
0, 8, 0, 0, 0, ...
0, 7, 1, 0, 0, ...
0, 0, 8, 0, 0, ...
0, 0, 7, 1, 0, ...
...
Then M^k converges to a single nonzero column giving the sequence.
The sequence with offset 1 divided by its aerated variant is (1, 8, 7, 0, 0, 0, ...). (End)
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n-1} 7^A000120(k).
a(n) = 1 + 7 * Sum_{k=1..n-1} A151785(k), for n >= 1.
a(2^n) = 2^(3n).
(End)
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MAPLE
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b:= proc(n) option remember; `if`(n<0, 0,
b(n-1)+x^add(i, i=Bits[Split](n)))
end:
a:= n-> subs(x=7, b(n-1)):
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MATHEMATICA
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A161342list[nmax_]:=Join[{0}, Accumulate[7^DigitCount[Range[0, nmax-1], 2, 1]]]; A161342list[100] (* Paolo Xausa, Aug 05 2023 *)
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CROSSREFS
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Cf. A160410, A160428, A161343, A006046, A130665, A116520, A130667, A116522, A116526, A116525, A360189.
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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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