cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A222173 Number of pentagons added at n-th stage to the structure of A222172.

Original entry on oeis.org

0, 1, 1, 1, 2, 3, 2, 1, 2, 4, 4, 3, 5, 7, 4, 1, 2, 4, 6, 8
Offset: 0

Views

Author

Omar E. Pol, Mar 21 2013

Keywords

Comments

Essentially the first differences of A222172.
Also number of P-toothpicks added at n-th stage to the P-toothpick structure of A222172.
First differs from A152978 at a(9).

Examples

			Apparently this is an irregular triangle:
0;
1, 1;
1, 2, 3, 2;
1, 2, 4, 4, 3, 5, 7, 4;
1, 2, 4, 6, 8,...

Links

Crossrefs

Cf. A139251, A152978, A222172, A222177, A222180, A222181.

Formula

a(n) = A222181(n+2)/10 = A222177(n+1)/2, n >= 1.

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

Original entry on oeis.org

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

Views

Author

Omar E. Pol, Mar 15 2013

Keywords

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

Crossrefs

Cf. A139250, A147562, A151723, A152968, A161330, A161644, A182632, A182840, A222172, A222176, A222181.

Formula

a(n) = 6 + 10*A222172(n-2), n >= 2. - Omar E. Pol, Nov 24 2013

Extensions

Name improved by Omar E. Pol, Nov 24 2013

A222176 Total number of ON states after n generations of cellular automaton based on pentagons starting near of the vertex of an infinite 72-degree wedge.

Original entry on oeis.org

0, 1, 3, 5, 7, 11, 17, 21, 23, 27, 35, 43, 49, 59, 73, 81, 83, 87, 95, 107, 123
Offset: 0

Views

Author

Omar E. Pol, Mar 21 2013

Keywords

Comments

The structure is one of the five wedges of A222180.
The sequence gives the number of pentagons in the structure after n-th stage. A222177 (the first differences) gives the number of pentagons added at n-th stage.
Also P-toothpick sequence starting near of the vertex of an infinite 72-degree wedge, since each pentagon can be replaced by a P-toothpick.
For more information see A222180.
First differs from A152998 at a(10).

Links

Crossrefs

Cf. A139250, A152998, A222172, A222177, A222180.

Formula

a(n) = (A222180(n+1) - 1)/5.

Extensions

Name improved by Omar E. Pol, Nov 24 2013
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.