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A161342 Number of "ON" cubic cells at n-th stage in simple 3-dimensional cellular automaton: a(n) = A160428(n)/8. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
First differences are in A161343. - Omar E. Pol, May 03 2015
From Gary W. Adamson, Aug 30 2016: (Start)
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)
LINKS
FORMULA
From Nathaniel Johnston, Nov 13 2010: (Start)
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)
a(n) = Sum_{k=0..floor(log_2(n))} 7^k*A360189(n-1,k). - Alois P. Heinz, Mar 06 2023
MAPLE
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)):
seq(a(n), n=0..44); # Alois P. Heinz, Mar 06 2023
MATHEMATICA
A161342list[nmax_]:=Join[{0}, Accumulate[7^DigitCount[Range[0, nmax-1], 2, 1]]]; A161342list[100] (* Paolo Xausa, Aug 05 2023 *)
CROSSREFS
Sequence in context: A167340 A037377 A166704 * A048732 A185038 A193490
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jun 14 2009
EXTENSIONS
More terms from Nathaniel Johnston, Nov 13 2010
STATUS
approved

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)