A151781 Partial sums of A151779.

1, 7, 13, 43, 49, 79, 109, 259, 265, 295, 325, 475, 505, 655, 805, 1555, 1561, 1591, 1621, 1771, 1801, 1951, 2101, 2851, 2881, 3031, 3181, 3931, 4081, 4831, 5581, 9331, 9337, 9367, 9397, 9547, 9577, 9727, 9877, 10627, 10657, 10807, 10957, 11707, 11857, 12607

Offset

1,2

Comments

Total number of ON cells after n-th generation of cellular automaton based on Z^3 lattice in the same way that A147562 is based on the Z^2 lattice. Here each cell has six neighbors.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

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, pp. 32-33.

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Mathematica

a[n_] := 6*5^(Total@ IntegerDigits[n - 1, 2] - 1); a[1] = 1; Accumulate@ Array[a, 46] (* Michael De Vlieger, Oct 31 2022 *)

Prog

(PARI) a(n)=sum(k=1, n, 6*5^(hammingweight(k-1)-1)\1) \\ Charles R Greathouse IV, Sep 14 2015

Crossrefs

Cf. A147562, A151779, A151790, A151792, A151793.

Sequence in context: A241718 A259184 A259186 * A224502 A361914 A047977

Adjacent sequences: A151778 A151779 A151780 * A151782 A151783 A151784

Keyword

nonn,look

Author

N. J. A. Sloane, Jun 25 2009

Status

approved