

A161336


Snowflake tree sequence: (A161330(n+1)  2)/6.


9



0, 1, 2, 3, 6, 7, 10, 13, 16, 21, 24, 29, 36, 37, 40, 43, 48, 57, 62, 75, 82, 91, 104, 111, 122, 135, 138, 145, 152, 161, 176, 187, 208, 223, 238, 255, 266, 279, 294, 309, 324, 333, 344, 363, 376, 397, 418, 435, 452, 475, 492, 519, 536, 555, 582, 603, 630, 649, 666, 683
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OFFSET

0,3


COMMENTS

This is an Etoothpick sequence. On a triangular graph paper consider an infinite 60degree wedge in which there is a single (and virtual) toothpick connected to its vertex. At stage 0 we start with no Etoothpicks. At stage 1 we place an Etoothpick, and so on. The sequence gives the number of Etoothpicks in the structure after n stages. A211974 (the first differences) gives the number added at the nth 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 Etoothpick (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

Table of n, a(n) for n=0..59.
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)1) for n >= 2.]
N. J. A. Sloane, A single Etoothpick
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Index entries for sequences related to toothpick sequences


FORMULA

a(n) = A213360(n)/6.  Omar E. Pol, Dec 20 2012


CROSSREFS

Cf. A139250, A161328, A161330, A161337, A161338, A211974, A213360.
Sequence in context: A069813 A266534 A293392 * A266536 A059096 A257678
Adjacent sequences: A161333 A161334 A161335 * A161337 A161338 A161339


KEYWORD

nonn


AUTHOR

Omar E. Pol, Jun 09 2009


EXTENSIONS

Extended and edited by Omar E. Pol, Dec 19 2012


STATUS

approved



