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 1-4 of 4 results.

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

A256641 a(n) is the total number of free ends of 5 line segments expansion at n iterations (see Comments lines for definition).

Original entry on oeis.org

5, 10, 10, 20, 40, 40, 20, 20, 40, 60, 70, 70, 100, 100, 40, 20, 40, 60, 80, 120
Offset: 1

Views

Author

Kival Ngaokrajang, Apr 06 2015

Keywords

Comments

The initial pattern consists of 5 straight line segments which are the radii of a regular pentagon. Their free ends are the ends of elements that do not contact or cross the other ones. Overlaps among different generations are prohibited except for one segment that connects between center points.
It appears that the sequence would be analog to 5*A032766 if the overlaps among different generations were prohibited without exception. See illustration in the links.
The terms of this sequence should be checked. - Omar E. Pol, Apr 13 2015

Links

Crossrefs

Cf. A032766, A222181.

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.

A222177 Number of pentagons added at n-th stage to the structure of A222176.

Original entry on oeis.org

0, 1, 2, 2, 2, 4, 6, 4, 2, 4, 8, 8, 6, 10, 14, 8, 2, 4, 8, 12, 16
Offset: 0

Views

Author

Omar E. Pol, Mar 21 2013

Keywords

Comments

Essentially the first differences of A222176.
Also number of P-toothpicks added at n-th stage to the P-toothpick structure of A222176.
First differs from A152968 at a(10).

Examples

			Apparently this is an irregular triangle:
0;
1;
2, 2;
2, 4, 6, 4;
2, 4, 8, 8, 6, 10, 14, 8;
2, 4, 8, 12, 16,...

Links

Crossrefs

Cf. A139251, A152968, A222173, A222176, A222180, A222181.

Formula

a(n) = A222181(n+1)/5, n >= 1.
Showing 1-4 of 4 results.

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

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