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A160379
Number of ON cells at n-th stage of three-dimensional version of the cellular automaton A160117 using cubes.
7
0, 1, 27, 35, 235, 261, 881, 937, 2241, 2339, 4591, 4743, 8207, 8425, 13365, 13661, 20341, 20727, 29411, 29899, 40851, 41453, 54937, 55665, 71945, 72811, 92151, 93167, 115831, 117009, 143261, 144613, 174717, 176255, 210475, 212211, 250811, 252757, 296001
OFFSET
0,3
COMMENTS
Each cell has 26 neighbors.
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.]
FORMULA
a(2n) = 46n^3 - 57n^2 + 57n - 19 for n>=1, a(2n+1) = 46n^3 - 51n^2 + 57n - 17 for n>=1. [Nathaniel Johnston, Nov 06 2010]
G.f.: x*(18*x^3+x^2+26*x+1)*(x^4+4*x^2+1) / ((x-1)^4*(x+1)^3). - Colin Barker, Feb 28 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, May 11 2009
EXTENSIONS
Edited by Omar E. Pol, Sep 05 2009
a(6) - a(27) from Nathaniel Johnston, Nov 06 2010
a(28) - a(38) from Colin Barker, Feb 28 2013
STATUS
approved