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

Author

N. J. A. Sloane, Jun 25 2009

Keywords

• nonn
• look

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

Crossrefs

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

Programs

Mathematica

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

PARI

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