A162797 - OEIS

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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.

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

(list; graph; refs; listen; history; text; internal format)

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.]

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

FORMULA

a(n) = A162796(n) - A162795(n).

EXAMPLE

Contribution from Omar E. Pol, Feb 22 2010: (Start)

If written as a triangle:

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.