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A162797
a(n) = difference between the number of toothpicks of A139250 that are orthogonal to the initial toothpick and the number of toothpicks that are parallel to the initial toothpick, after n even rounds.
9
1, 1, 5, 1, 5, 5, 17, 1, 5, 5, 17, 5, 17, 21, 49, 1, 5, 5, 17, 5, 17, 21, 49, 5, 17, 21, 49, 21, 53, 81, 129, 1, 5, 5, 17, 5, 17, 21, 49, 5, 17, 21, 49, 21, 53, 81, 129, 5, 17, 21, 49, 21, 53, 81, 129
OFFSET
1,3
COMMENTS
It appears that a(2^k) = 1, for k >= 0. [From Omar E. Pol, Feb 22 2010]
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 1..94
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(n) = A162796(n) - A162795(n).
EXAMPLE
Contribution from Omar E. Pol, Feb 22 2010: (Start)
If written as a triangle:
1;
1,5;
1,5,5,17;
1,5,5,17,5,17,21,49;
1,5,5,17,5,17,21,49,5,17,21,49,21,53,81,129;
1,5,5,17,5,17,21,49,5,17,21,49,21,53,81,129,5,17,21...
Rows converge to A173464.
(End)
Contribution from Omar E. Pol, Apr 01 2011 (Start):
It appears that the final terms of rows give A000337.
It appears that row sums give A006516.
(End)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jul 14 2009
EXTENSIONS
Edited by Omar E. Pol, Jul 18 2009
More terms from Omar E. Pol, Feb 22 2010
More terms (a(51)-a(55)) from Nathaniel Johnston, Mar 30 2011
STATUS
approved