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

0,2

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

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

Mathematica

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

Crossrefs

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

Sequence in context: A345946 A161146 A208380 * A074102 A118719 A134739

Adjacent sequences: A160425 A160426 A160427 * A160429 A160430 A160431

Keyword

nonn

Author

Omar E. Pol, Jun 01 2009

Extensions

Formulas and more terms from Nathaniel Johnston, Nov 13 2010

More terms from Michael De Vlieger, Nov 01 2022

Status

approved