

A220478


Equilateral triangle from the snowflake (or Etoothpick) structure of A161330 (see Comments lines for definition).


3



0, 2, 4, 6, 10, 12, 16, 20, 24, 30, 34, 40, 48, 50, 54, 58, 64, 74, 80, 94, 102, 112, 126, 134, 146, 160, 164, 172, 180, 190, 206, 218, 240, 256, 272, 290, 302, 316, 332, 348, 364, 374, 386, 406, 420, 442, 464, 482, 500, 524, 542, 570, 588, 608, 636, 658, 686, 706, 724, 742
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OFFSET

0,2


COMMENTS

It appears that if n >> 1 the structure looks like an equilateral triangle, which is essentially one of the six wedges of the Etoothpick (or snowflake) structure of A161330. The sequence gives the number of Etoothpicks in the structure after n stages. A220498 (the first differences) gives the number added at the nth round. For more information and some illustrations see A161330. For the Etoothpick right triangle see A211964.


REFERENCES

Mohammad K. Azarian, A Trigonometric Characterization of Equilateral Triangle, Problem 336, Mathematics and Computer Education, Vol. 31, No. 1, Winter 1997, p. 96. Solution published in Vol. 32, No. 1, Winter 1998, pp. 8485.
Mohammad K. Azarian, Equating Distances and Altitude in an Equilateral Triangle, Problem 316, Mathematics and Computer Education, Vol. 28, No. 3, Fall 1994, p. 337. Solution published in Vol. 29, No. 3, Fall 1995, pp. 324325.


LINKS

Table of n, a(n) for n=0..59.
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 cellular automata
Index entries for sequences related to toothpick sequences


FORMULA

a(n) = n + (A161330(n)  2)/6, n >= 1.
a(n) = n + A161336(n) = 2*A211964(n).


CROSSREFS

Cf. A139250, A161328, A160120, A161330, A161336, A211964, A213360, A220498.
Sequence in context: A005942 A024907 A033098 * A033868 A045954 A072542
Adjacent sequences: A220475 A220476 A220477 * A220479 A220480 A220481


KEYWORD

nonn


AUTHOR

Omar E. Pol, Dec 22 2012


STATUS

approved



