%I
%S 0,1,6,16,26,36,56,86,106,116,136,176,216,246,296,366,406,416,436,476,
%T 536,616
%N Total number of ON states after n generations of cellular automaton based on pentagons. Also Ptoothpick sequence (see Comments lines for definition).
%C 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.
%C 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).
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poltp055.jpg">Illustration of structure after 5 stages</a>, (Contains 36 pentagons).
%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) = 6 + 10*A222172(n2), n >= 2.  _Omar E. Pol_, Nov 24 2013
%Y Cf. A139250, A147562, A151723, A152968, A161330, A161644, A182632, A182840, A222172, A222176, A222181.
%K nonn,more
%O 0,3
%A _Omar E. Pol_, Mar 15 2013
%E Name improved by _Omar E. Pol_, Nov 24 2013
