A160428 Number of ON cells at n-th stage of three-dimensional version of the cellular automaton A160410, using cubes.

0, 8, 64, 120, 512, 568, 960, 1352, 4096, 4152, 4544, 4936, 7680, 8072, 10816, 13560, 32768, 32824, 33216, 33608, 36352, 36744, 39488, 42232, 61440, 61832, 64576, 67320, 86528, 89272, 108480, 127688, 262144, 262200, 262592, 262984, 265728, 266120, 268864, 271608

Offset: 0

Author

Omar E. Pol, Jun 01 2009

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..1000
• 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.]
• Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, p. 33.
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A139250, A160119, 160379, A160410, A160429, A161340, A161342.

Programs

Mathematica

a[n_] := 8*Sum[7^DigitCount[k, 2, 1], {k, 0, n - 1}]; Array[a, 40, 0] (* Michael De Vlieger, Nov 01 2022 *)

Formula

a(n) = 8 * Sum_{k=0..n-1} 7^A000120(k)

a(n) = 8 + 56 * Sum_{k=1..n-1} A151785(k) for n >= 1

Extensions

Formulas and more terms from Nathaniel Johnston, Nov 13 2010

More terms from Michael De Vlieger, Nov 01 2022