A161336 Snowflake tree sequence: (A161330(n+1) - 2)/6.

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

Offset: 0

Author

Omar E. Pol, Jun 09 2009

Keywords

• nonn

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
• Index entries for sequences related to toothpick sequences

Crossrefs

Cf. A139250, A161328, A161330, A161337, A161338, A211974, A213360.

Formula

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

Extensions

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