A186411 First differences of A186410.

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

Author

Omar E. Pol, Feb 21 2011

Keywords

• nonn

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.]
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS.
• Index entries for sequences related to cellular automata.

Crossrefs

Cf. A000120, A147582, A151779, A186410.

Programs

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 *)

Formula

a(n) = 1 + 4*5^(A000120(n-1)-1), n >= 2. - Nathaniel Johnston, Mar 22 2011

Extensions

More terms from Nathaniel Johnston, Mar 22 2011

More terms from Amiram Eldar, Aug 01 2023