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Search: a161341 -id:a161341
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Number of "ON" cells at n-th stage of three-dimensional version of the cellular automaton A160414 using cubes.
+10
5
0, 1, 27, 83, 343, 399, 791, 1183, 3375, 3431, 3823, 4215, 6959, 7351, 10095, 12839, 29791, 29847, 30239, 30631, 33375, 33767, 36511, 39255, 58463, 58855, 61599, 64343, 83551, 86295, 105503, 124711, 250047, 250103, 250495, 250887, 253631, 254023, 256767, 259511
OFFSET
0,3
COMMENTS
For the first differences see A161341, where an explicit formula is given.
LINKS
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
FORMULA
a(n) = (2n-1)^3 if n is a power of 2.
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jun 14 2009
EXTENSIONS
Edited by Omar E. Pol, Sep 05 2009, Nov 21 2010
More terms from Nathaniel Johnston, Nov 15 2010
More terms from Jinyuan Wang, Mar 14 2020
STATUS
approved
Fractal triangle whose virtual skeleton is a polyedge as the Y-toothpick structure of A160120.
+10
5
0, 9, 33, 57, 123, 147
OFFSET
0,2
COMMENTS
Number of ON states after n generations of cellular automaton based on the infinite triangular grid.
LINKS
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
CROSSREFS
KEYWORD
more,nonn
AUTHOR
Omar E. Pol, Jun 17 2009
STATUS
approved

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