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A186411
First differences of A186410.
1
0, 1, 5, 5, 21, 5, 21, 21, 101, 5, 21, 21, 101, 21, 101, 101, 501, 5, 21, 21, 101, 21, 101, 101, 501, 21, 101, 101, 501, 101, 501, 501, 2501, 5, 21, 21, 101, 21, 101, 101, 501, 21, 101, 101, 501, 101, 501, 501, 2501, 21, 101, 101, 501, 101, 501, 501, 2501, 101
OFFSET
0,3
COMMENTS
Number of cells turned "ON" at h-th stage of the three-dimensional cellular automaton of A186410. In other words: number of cubes added at n-th stage to the structure of A186410.
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) = 1 + 4*5^(A000120(n-1)-1), n >= 2. - Nathaniel Johnston, Mar 22 2011
MATHEMATICA
a[n_] := 1 + 4*5^(DigitCount[n-1, 2, 1]-1); a[0] = 0; a[1] = 1; Array[a, 100, 0] (* Amiram Eldar, Aug 01 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Feb 21 2011
EXTENSIONS
More terms from Nathaniel Johnston, Mar 22 2011
More terms from Amiram Eldar, Aug 01 2023
STATUS
approved