OFFSET
0,3
COMMENTS
This is an E-toothpick sequence. On a triangular graph paper consider an infinite 60-degree wedge in which there is a single (and virtual) toothpick connected to its vertex. At stage 0 we start with no E-toothpicks. At stage 1 we place an E-toothpick, and so on. The sequence gives the number of E-toothpicks in the structure after n stages. A211974 (the first differences) gives the number added at the n-th stage. The structure is the tree that arise from one of the six spokes of the structure of A213360 which is essentially the same as the E-toothpick (or snowflake) structure of A161330. For n >> 1 the structure looks like a quadrilateral formed by two scalene right triangles which are joined at their hypotenuses. - Omar E. Pol, Dec 19 2012
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, A single E-toothpick
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
FORMULA
a(n) = A213360(n)/6. - Omar E. Pol, Dec 20 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jun 09 2009
EXTENSIONS
Extended and edited by Omar E. Pol, Dec 19 2012
STATUS
approved