

A222180


Total number of ON states after n generations of cellular automaton based on pentagons. Also Ptoothpick sequence (see Comments lines for definition).


5



0, 1, 6, 16, 26, 36, 56, 86, 106, 116, 136, 176, 216, 246, 296, 366, 406, 416, 436, 476, 536, 616
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OFFSET

0,3


COMMENTS

Analog of A161644, A147562 and A151723, but here we are working without a lattice. Each regular pentagon has five virtual neighbors. Overlapping are prohibited. The sequence gives the number of pentagons in the structure after nth stage. A222181 (the first differences) gives the number of pentagons added at nth stage.
Also this is a Ptoothpick sequence since every pentagon can be replaced by a Ptoothpick which is formed by five toothpicks as a fivepointed star. Note that each toothpick can be represented as an apothem or as a radius of a pentagon. In both types of structures the number of toothpicks after nth stage is equal to 5*a(n).


LINKS

Table of n, a(n) for n=0..21.
Omar E. Pol, Illustration of structure after 5 stages, (Contains 36 pentagons).
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) = 6 + 10*A222172(n2), n >= 2.  Omar E. Pol, Nov 24 2013


CROSSREFS

Cf. A139250, A147562, A151723, A152968, A161330, A161644, A182632, A182840, A222172, A222176, A222181.
Sequence in context: A017341 A232491 A191157 * A212905 A191117 A265389
Adjacent sequences: A222177 A222178 A222179 * A222181 A222182 A222183


KEYWORD

nonn,more


AUTHOR

Omar E. Pol, Mar 15 2013


EXTENSIONS

Name improved by Omar E. Pol, Nov 24 2013


STATUS

approved



