A161336 - OEIS

%I #24 Feb 24 2021 02:48:18

%S 0,1,2,3,6,7,10,13,16,21,24,29,36,37,40,43,48,57,62,75,82,91,104,111,

%T 122,135,138,145,152,161,176,187,208,223,238,255,266,279,294,309,324,

%U 333,344,363,376,397,418,435,452,475,492,519,536,555,582,603,630,649,666,683

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

%C 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

%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, 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.]

%H N. J. A. Sloane, <a href="/A161330/a161330.jpg">A single E-toothpick</a>

%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>

%H <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>

%F a(n) = A213360(n)/6. - _Omar E. Pol_, Dec 20 2012

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

%K nonn

%O 0,3

%A _Omar E. Pol_, Jun 09 2009

%E Extended and edited by _Omar E. Pol_, Dec 19 2012