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 1-5 of 5 results.

A222181 Number of pentagons added at n-th stage to the structure of A222180.

Original entry on oeis.org

0, 1, 5, 10, 10, 10, 20, 30, 20, 10, 20, 40, 40, 30, 50, 70, 40, 10, 20, 40, 60, 80
Offset: 0

Views

Author

Omar E. Pol, Mar 15 2013

Keywords

Comments

Essentially the first differences of A222180.
Also number of P-toothpicks added at n-th stage to the P-toothpick structure of A222180.

Examples

			Apparently this is an irregular triangle:
0;
1;
5;
10,10;
10,20,30,20;
10,20,40,40,30,50,70,40;
10,20,40,60,80,...
		

Crossrefs

Formula

a(n) = 10*A222173(n-2), n >= 3. - Omar E. Pol, Nov 24 2013

A222172 Total number of ON states after n generations of cellular automaton based on pentagons starting near of the vertex of an infinite 36-degree wedge.

Original entry on oeis.org

0, 1, 2, 3, 5, 8, 10, 11, 13, 17, 21, 24, 29, 36, 40, 41, 43, 47, 53, 61
Offset: 0

Views

Author

Omar E. Pol, Mar 21 2013

Keywords

Comments

The sequence gives the number of pentagons in the structure after n-th stage. A222173 (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 36-degree wedge, since each pentagon can be replaced by a P-toothpick.
For more information see A222180.
First differs from A153000 at a(9).

Crossrefs

Formula

a(n) = (((A222180(n+2) - 1)/5) - 1)/2 = (A222176(n+1) - 1)/2.
a(n) = (A222180(n+2) - 6)/10. - Omar E. Pol, Nov 24 2013

Extensions

Name improved by Omar E. Pol, Nov 24 2013

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,...
		

Crossrefs

Formula

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

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).

Crossrefs

Formula

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

Extensions

Name improved by Omar E. Pol, Nov 24 2013

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,...
		

Crossrefs

Formula

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