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.

Previous Showing 41-48 of 48 results.

A253771 First differences of A253770.

Original entry on oeis.org

0, 6, 18, 18, 54, 18, 54, 54, 126, 54, 54, 54, 126, 90, 126, 162, 306, 162, 54, 54, 126, 90, 126, 162, 306, 198, 126, 162, 306, 306, 342, 414, 702, 486, 126, 54, 126, 90, 126, 162, 306, 198, 126, 162, 306, 306, 342, 414, 702, 522, 198, 162
Offset: 0

Views

Author

Omar E. Pol, Jan 13 2015

Keywords

Comments

Number of cells turned "ON" at n-th stage of cellular automaton of A253770.
Also 6 times the number of Y-toothpicks added at n-th stage in the Y-toothpick structure of A160120.

Examples

			Positive terms can be written as a triangle in which row lengths is A011782 as shown below:
6;
18;
18,  54;
18,  54,54,126;
54,  54,54,126,90,126,162,306;
162, 54,54,126,90,126,162,306,198,126,162,306,306,342,414,702;
486,126,54,126,90,126,162,306,198,126,162,306,306,342,414,702,522,198,162,...

Links

Crossrefs

Cf. A139251, A147582, A151724, A160121, A161645, A182633, A250301, A253770.

Formula

a(n) = 6*A160121(n).

A266533 First differences of A266532.

Original entry on oeis.org

1, 3, 3, 9, 3, 9, 9, 21, 3, 9, 9, 21, 9, 21, 21, 45, 3, 9, 9, 21, 9, 21, 21, 45, 9, 21, 21, 45, 21, 45, 45, 93, 3, 9, 9, 21, 9, 21, 21, 45, 9, 21, 21, 45, 21, 45, 45, 93, 9, 21, 21, 45, 21, 45, 45, 93, 21, 45, 45, 93, 45, 93, 93, 189, 3, 9, 9, 21, 9, 21, 21, 45, 9, 21, 21, 45, 21, 45, 45, 93
Offset: 1

Views

Author

David Applegate and Omar E. Pol, Jan 18 2016

Keywords

Comments

Number of Y-toothpicks added at n-th stage in the structure of A266532.
A simplified version of A160121.

Examples

			Written as an irregular triangle in which the row lengths are the terms of A011782 the sequence begins:
1;
3;
3, 9;
3, 9, 9, 21;
3, 9, 9, 21, 9, 21, 21, 45;
3, 9, 9, 21, 9, 21, 21, 45, 9, 21, 21, 45, 21, 45, 45, 93;
...
Observation: at least the first 11 terms of the right border coincide with A068156.

Links

Crossrefs

Cf. A000120, A011782, A038573, A068156. A139251, A147582, A160121, A151710, A160721, A266532, A267701.

Formula

a(1) = 1. It appears that a(n) = 3*A038573(n-1), n >= 2.

A161910 Y-toothpick sequence starting at the corner of an infinite hexagon from which protrudes a half toothpick with an angle = Pi/6.

Original entry on oeis.org

0, 1, 2, 5, 6, 9, 12, 19, 22, 25, 28, 35, 40, 47, 56, 73
Offset: 0

Views

Author

Omar E. Pol, Jun 21 2009

Keywords

Comments

The sequence gives the number of Y-toothpicks in the structure after n rounds. A160123 (the first differences) gives the number added at the n-th round.
See the entries A160120, A161830 and A161426 for more information about Y-toothpick sequences.

Links

Crossrefs

Cf. A160120, A160121, A160123, A160406, A161426, A161830, A161831.

Formula

a(n) = (A160120(n+1)-1)/3.

A177241 First differences of A177240.

Original entry on oeis.org

0, 1, 4, 4, 16, 4, 16
Offset: 0

Views

Author

Omar E. Pol, May 05 2010

Keywords

Comments

Question: Is this the same as A102376 but starting with zero? (See also the main question in the entry A177240).

Links

Crossrefs

Cf. A102376, A116520, A139250, A139251, A160121.

A250301 First differences of A250300.

Original entry on oeis.org

0, 3, 3, 6, 12, 12, 6, 12, 18, 18, 18, 18, 36, 36, 12, 24, 30, 18, 18, 24, 42, 54, 42, 36, 60, 66, 54, 48, 90, 90, 30, 54, 54, 18, 18, 24, 42, 54, 42, 42, 66, 78, 78, 78, 114, 150, 102, 72, 108
Offset: 0

Views

Author

Omar E. Pol, Jan 17 2015

Keywords

Comments

Number of cells turned "ON" at n-th stage of cellular automaton of A250300.
Compare A161645.

Examples

			Positive terms can be written as a triangle in which row lengths is A011782 as shown below:
3;
3;
6,  12;
12,  6, 12, 18;
18, 18, 18, 36, 36, 12, 24, 30;
18, 18, 24, 42, 54, 42, 36, 60, 66, 54, 48, 90, 90, 30, 54, 54;
18, 18, 24, 42, 54, 42, 42, 66, 78, 78, 78, 114, 150, 102, 72, 108, ...

Links

Crossrefs

Cf. A139251, A147582, A151724, A160121, A161645, A182633, A250300, A253771.

A355311 Number of V-toothpicks added at n-th stage to the V-toothpick structure of A355310.

Original entry on oeis.org

1, 2, 4, 6, 8, 6, 10, 14, 18, 10, 10, 14, 20, 18, 24, 36, 44, 22
Offset: 1

Views

Author

Jean Hoffmann and Omar E. Pol, Jul 20 2022

Keywords

Comments

An idea from Jean Hoffmann.

Examples

			Written as an irregular triangle in which the row lengths give 1 together with A011782 the sequence begins:
   1;
   2;
   4;
   6,  8;
   6, 10, 14, 18;
  10, 10, 14, 20, 18, 24, 36, 44;
   ...

Links

Crossrefs

First differences of A355310.
Cf. A011782, A139251, A160121, A161207, A161413, A161421, A296612, A299477, A299479.

A161327 a(n) = A161326(n)/3.

Original entry on oeis.org

3, 7, 5, 7, 9, 17, 11, 7, 9, 17, 17, 19, 23, 39, 29, 11, 9, 17, 17, 19, 25, 43, 39, 25, 23, 39, 45
Offset: 1

Views

Author

Omar E. Pol, Jun 18 2009

Keywords

Links

Crossrefs

Cf. A160120, A160121, A161326.

Extensions

More terms from Amiram Eldar, May 10 2024

A173465 a(n) = A151710(n+1)/3.

Original entry on oeis.org

1, 1, 3, 1, 3, 3, 7, 1, 3, 3, 7, 5, 7, 9, 17, 1, 3, 3, 7, 5, 7, 9, 17, 7, 7, 9, 17, 17, 19, 23, 39, 1
Offset: 1

Views

Author

Omar E. Pol, May 29 2010

Keywords

Comments

First 23 terms the same as A151837.

Examples

			If written as a triangle, begins:
1;
1,3;
1,3,3,7;
1,3,3,7,5,7,9,17;
1,3,3,7,5,7,9,17,7,7,9,17,17,19,23,39;

Links

Crossrefs

Cf. A139251, A151837, A160120, A160121, A160123.
Previous Showing 41-48 of 48 results.

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