A222180 Total number of ON states after n generations of cellular automaton based on pentagons. Also P-toothpick sequence (see Comments lines for definition).

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

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 n-th stage. A222181 (the first differences) gives the number of pentagons added at n-th stage.

Also this is a P-toothpick sequence since every pentagon can be replaced by a P-toothpick which is formed by five toothpicks as a five-pointed 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 n-th 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(n-2), 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 * A341400 A367295 A212905

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