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A173457
Number of cell turned "ON" at n-th stage of cellular automaton of A173456.
5
0, 1, 8, 12, 4, 28, 36, 4, 28, 36, 12, 84, 108, 4, 28, 36, 12, 84, 108, 12, 84, 108, 36, 252, 324, 4, 28, 36, 12, 84, 108, 12, 84, 108, 36, 252, 324, 12, 84, 108, 36, 252, 324, 36, 252, 324, 108, 756, 972, 4, 28, 36, 12, 84, 108, 12, 84, 108, 36, 252, 324
OFFSET
0,3
COMMENTS
Essentially the first differences of A173456.
It appears that row lengths give A098011. After the initial zero, it appears that row lengths give the absolute values of A110164. - Omar E. Pol, Apr 22 2013
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(0)=0, a(1)=1, a(2)=8, a(3)=12, for n>=4 when (n MOD 3)=0,1,2 let m=36,4,28 then a(n)=m*A147610((n + 2) / 3). (Found empirically) [Lars Blomberg, Apr 22 2013]
EXAMPLE
From Omar E. Pol, Apr 22 2013 (Start):
When written as an irregular triangle begins:
0;
1;
8,12;
4,28,36;
4,28,36,12,84,108;
4,28,36,12,84,108,12,84,108,36,252,324;
4,28,36,12,84,108,12,84,108,36,252,324,12,84,108,36,252,324,36,252,324,108,756,972;
4,28,36,12,84,108,12,84,108,36,252,324,...
(End)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Feb 18 2010
EXTENSIONS
a(41)-a(60) from Lars Blomberg, Apr 22 2013
STATUS
approved