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.

A160731 First differences of A160730.

Original entry on oeis.org

2, 2, 4, 6, 6, 6, 12, 14, 12, 6, 12, 14, 16, 18, 32, 34, 20, 6, 12, 14, 16, 18, 32, 34, 24, 18, 32, 38, 44, 62, 92, 82, 36, 6, 12, 14, 16, 18, 32, 34, 24, 18, 32, 38, 44, 62, 92, 82, 40, 18, 32, 38, 44, 62
Offset: 1

Views

Author

Omar E. Pol, May 25 2009

Keywords

Examples

			Placing the entries starting from a(4) in a triangle with rows that have length equal to powers of two gives:
6, 6
6, 12, 14, 12
6, 12, 14, 16, 18, 32, 34, 20
6, 12, 14, 16, 18, 32, 34, 24, 18, 32, 38, 44, 62, 92, 82, 36
...
The rows of this triangle tend to 2*A168114.

Links

Crossrefs

Cf. A139250, A139251, A160730, A160733, A160737, A160739, A160741.

Formula

From Nathaniel Johnston, Mar 28 2011: (Start)
a(n) = 2*A168113(n)
a(2^(n+2) + 1) = 4(2^n + 1), n >= 1.
(End)

Extensions

Terms after a(11) from Nathaniel Johnston, Mar 28 2011

A168112 Toothpick sequence starting with a straight line, with angle = Pi/4, from which protrudes a half toothpick.

Original entry on oeis.org

0, 1, 2, 4, 7, 10, 13, 19, 26, 32, 35, 41, 48, 56, 65, 81, 98, 108, 111, 117, 124, 132, 141, 157, 174, 186, 195, 211, 230, 252, 283, 329, 370, 388, 391, 397, 404, 412, 421, 437, 454, 466, 475, 491, 510, 532, 563, 609, 650, 670
Offset: 0

Views

Author

Omar E. Pol, Dec 07 2009

Keywords

Comments

On the infinite square grid, we start at round 0 drawing a straight line, with angle = Pi/4, from which protrudes a half toothpick.
At round 1 we place an orthogonal toothpick centered at the end.
In each subsequent round, for every exposed toothpick end, place an orthogonal toothpick centered at that end.
The sequence gives the number of toothpicks after n rounds.
See also A168113, the first differences.
For more information see A139250, which is the main entry for this sequence.

Links

Crossrefs

Cf. A139250, A139251, A153000, A153006, A160406, A168113, A168114.

Formula

a(n) = A160730(n)/2. [From Nathaniel Johnston, Mar 28 2011]

Extensions

Terms after a(34) from Nathaniel Johnston, Mar 28 2011

A168113 First differences of A168112.

Original entry on oeis.org

1, 1, 2, 3, 3, 3, 6, 7, 6, 3, 6, 7, 8, 9, 16, 17, 10, 3, 6, 7, 8, 9, 16, 17, 12, 9, 16, 19, 22, 31, 46, 41, 18, 3, 6, 7, 8, 9, 16, 17, 12, 9, 16, 19, 22, 31, 46, 41, 20, 9, 16, 19, 22, 31, 46, 43, 30, 31, 48
Offset: 1

Views

Author

Omar E. Pol, Dec 07 2009

Keywords

Comments

a(n) is the number of toothpicks added at the n-th round in the toothpick structure of A168112.

Examples

			If written as a triangle, begins:
1;
1;
2;
3,3;
3,6,7,6;
3,6,7,8,9,16,17,10;
3,6,7,8,9,16,17,12,9,16,19,22,31,46,41,18;
Rows converge to A168114.

Links

Crossrefs

Cf. A139250, A139251, A152978, A152980, A160407, A168112, A168114.

Formula

Observation: It appears that a(2^i+2) = 3, for i>0.
a(n) = A160731(n)/2. [From Nathaniel Johnston, Mar 28 2011]

Extensions

Terms after a(34) from Nathaniel Johnston, Mar 28 2011
Showing 1-3 of 3 results.

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

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