



0, 4, 12, 24, 36, 52, 80, 112, 132, 148, 176, 212, 252, 312, 400, 480, 516, 532, 560, 596, 636, 696, 784, 868, 924, 984, 1076, 1188, 1328, 1536, 1792, 1984, 2052, 2068, 2096, 2132, 2172, 2232, 2320, 2404, 2460, 2520, 2612, 2724, 2864, 3072, 3328, 3524, 3612
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OFFSET

0,2


COMMENTS

For the first differences see A147646.  Omar E. Pol, Jul 24 2009
It appears that a(n) is also the total path length of a toothpick structure as A139250 after nth stage which is constructed following a special rule: toothpicks of the new generation have length 4 when are placed on the square grid (note that every toothpick has four components of length 1), but after every stage, one (or two) of the four components of every toothpick of the new generation is removed, if such component contains a endpoint of the toothpick and if such endpoint is touching the midpoint or the endpoint of another toothpick. The truncated endpoints of the toothpicks remain exposed forever. Note that there are three sizes of toothpicks in the structure: toothpicks of length 4, 3 and 2. a(n) is also the total number of components in the structure after nth stage. a(n) is also the number of grid points that are covered after nth stage, except the central point of the structure. The toothpick sequence A139250 gives the number of toothpicks after nth stage.  Omar E. Pol, Oct 24 2011


LINKS

Table of n, a(n) for n=0..48.
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, Catalog of Toothpick and Cellular Automata Sequences in the OEIS


CROSSREFS

Cf. A139250, A139251, A152980, A153006, A159793, A159794.
Cf. A147646, A152980.  Omar E. Pol, Jul 24 2009
Sequence in context: A071228 A304077 A108997 * A301171 A033602 A301175
Adjacent sequences: A159792 A159793 A159794 * A159796 A159797 A159798


KEYWORD

nonn


AUTHOR

Omar E. Pol, May 02 2009


EXTENSIONS

More terms from Omar E. Pol, Jul 24 2009


STATUS

approved



