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A151781
Partial sums of A151779.
7
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.
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
KEYWORD
nonn,look
AUTHOR
N. J. A. Sloane, Jun 25 2009
STATUS
approved