OFFSET
0,3
COMMENTS
Each cell has 26 neighbors.
Differs from A160379 in the same way that A160118 differs from A160117. - N. J. A. Sloane, Jan 01 2010
LINKS
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.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS.
FORMULA
From Nathaniel Johnston, Mar 24 2011: (Start)
In general, a d-dimensional version of the cellular automaton A160118 has its cell count given by the following formulas (where wt(k) = A000120(k)):
a(2n-1) = 3^d + (2^d)*Sum_{k=1..n-1}(2^d-1)^(wt(k)-1) + (2^d)*(3^d-2)*Sum_{k=1..n-2}(2^d-1)^(wt(k)-1), n >= 2.
a(2n) = 3^d + (2^d)*Sum_{k=1..n-1}(2^d-1)^(wt(k)-1) + (2^d)*(3^d-2)*Sum_{k=1..n-1}(2^d-1)^(wt(k)-1), n >= 1. (End)
MATHEMATICA
With[{d = 3}, wt[n_] := DigitCount[n, 2, 1]; a[n_] := If[OddQ[n], 3^d + (2^d)*Sum[(2^d - 1)^(wt[k] - 1), {k, 1, (n - 1)/2}] + (2^d)*(3^d - 2)*Sum[(2^d - 1)^(wt[k] - 1), {k, 1, (n - 3)/2}], 3^d + (2^d)*Sum[(2^d - 1)^(wt[k] - 1), {k, 1, n/2 - 1}] + (2^d)*(3^d - 2)*Sum[(2^d - 1)^(wt[k] - 1), {k, 1, n/2 - 1}]]; a[0] = 0; a[1] = 1; Array[a, 50, 0]] (* Amiram Eldar, Aug 01 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, May 05 2009
EXTENSIONS
More terms from Omar E. Pol, May 11 2009
Edited by N. J. A. Sloane, Sep 05 2009
a(8)-a(32) from Nathaniel Johnston, Mar 24 2011
More terms from Amiram Eldar, Aug 01 2023
STATUS
approved