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 11-20 of 22 results. Next

A160171 First differences of X-toothpicks numbers A160170.

Original entry on oeis.org

0, 1, 4, 8, 8, 24, 32, 32, 56, 80, 80, 88, 112, 160, 168, 240, 224, 344, 320, 320, 344, 448, 528, 536, 704, 704, 872, 736, 880, 840, 1024, 1088, 1256, 1328, 1392, 1416, 1440, 1504, 1656
Offset: 0

Views

Author

Omar E. Pol, May 03 2009, Dec 13 2010

Keywords

Comments

Number of X-toothpicks added at n-th stage to the three-dimensional X-toothpick structure of A160170.
For another version see A170875.

Links

Crossrefs

X-toothpick sequence: A160170.
Cf. A139250, A139251, A160120, A160121, A160160, A160161, A170875.

Extensions

More terms (a(6)-a(38)) based on Email from R. J. Mathar dated on Jan 10 2010.

A160409 First differences of toothpick numbers A160408.

Original entry on oeis.org

1, 1, 2, 4, 4, 4, 4, 4, 8, 16, 16, 8, 4, 4, 8
Offset: 1

Views

Author

Omar E. Pol, May 23 2009

Keywords

Comments

Number of toothpick added to the toothpick pyramid at the round n.
See also the toothpick sequences A139250, A160160 and the toothpick triangle A160406.

Examples

			Contribution from _Omar E. Pol_, Jun 06 2009: (Start)
Array begins:
========
x, y, z
========
1, 1, 2;
4, 4, 4;
4, 4, 8;
16, 16, 8;
4, 4, 8;
(End)

Links

Crossrefs

Cf. A139250, A139251, A160160, A160161, A160406, A160407, A160408.

Extensions

More terms from Omar E. Pol, Jun 06 2009

A170876 Number of toothpicks after n stages of 3-D toothpick structure defined in Comments.

Original entry on oeis.org

0, 1, 5, 21, 37, 53, 117, 197, 261, 405, 565, 789, 965, 1221, 1541, 1941, 2453, 2933, 3621, 4389, 5093, 5909, 6805, 7925, 9093, 10629, 12197, 14133, 15733, 17717, 19493, 21605, 23909, 26453, 29109, 32117, 35013, 38085, 41285
Offset: 0

Views

Author

N. J. A. Sloane, Jan 05 2010, based on email from R. J. Mathar, Jun 02 2009 Revised by R. J. Mathar, Jan 08 2010, Jan 09 2010

Keywords

Comments

We are in 3-D, and we are placing ordinary toothpicks, as in A139250.
We start with one toothpick in the z direction
We place toothpicks at any free end, as in A139250.
We always place new toothpicks in pairs, two perpendicular toothpicks that are perpendicular to the original toothpick
The toothpicks are always in 2 out of the 3 (x, y or z) directions.
The initial values are as follows (this should be checked!):
n:.0..1..2..3..4..5..6
----------------------------
x..0..0..2..4..8..4.24 (Number added in x direction)
y..0..0..2..4..8..4.24 (Number added in y direction)
z..0..1..0..8..0..8.16 (Number added in z direction)
----------------------------
...0..1..4.16.16.16.64 (Total number added at n-th stage, A170876)
----------------------------
a..0..1..5.21.37.53.117 (Total so far, this sequence)
----------------------------

Examples

			At stage 2 we have a horizontal cross, a vertical toothpick then another horizontal cross, for a total of 5 toothpicks.
Then we add 8 vertical toothpicks at the ends of the crosses and 8 horizontal toothpicks in the same planes as the crosses, for a total of 21 toothpicks.

Links

Crossrefs

Cf. A139250, A170875 (first differences), A160160, A160170. For another version see A170837.

A161210 Toothpick sequence starting at the outside corner of an infinite cube from which protrudes a half toothpick.

Original entry on oeis.org

0, 1, 3, 7, 14, 21, 28
Offset: 0

Views

Author

Omar E. Pol, Jun 06 2009

Keywords

Comments

The sequence gives the number of toothpicks after n rounds. A161211 (the first differences) gives the number added at the n-th round.
This structure is a three-dimensional version of the toothpick structure of A153006.
Toothpicks are placed following a rotation of axes: x,y,z,x,y,z,... and so on.
See A139250 and A160160 for more information about the toothpick sequences.

Links

Crossrefs

Cf. A139250, A152980, A153006, A160160, A161211, A161212, A161214, A161216.

A161212 a(n) = A161210(n)*2.

Original entry on oeis.org

0, 2, 6, 14, 28, 42, 56
Offset: 0

Views

Author

Omar E. Pol, Jun 06 2009

Keywords

Links

Crossrefs

Cf. A139250, A152980, A153006, A160160, A161210, A161213, A161214, A161216.

A161214 a(n) = A161210(n)*3.

Original entry on oeis.org

0, 3, 9, 21, 42, 63, 84
Offset: 0

Views

Author

Omar E. Pol, Jun 06 2009

Keywords

Links

Crossrefs

Cf. A139250, A152980, A153006, A160160, A161210, A161212, A161215, A161216.

A161216 a(n) = A161210(n)*4.

Original entry on oeis.org

0, 4, 12, 28, 56, 84, 112
Offset: 0

Views

Author

Omar E. Pol, Jun 06 2009

Keywords

Links

Crossrefs

Cf. A139250, A152980, A153006, A160160, A161210, A161212, A161214, A161217.

A160418 a(n) = A160407(n+2)/2.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 3, 5, 4, 1, 1, 2, 2, 2, 3, 5, 4, 2, 3, 5, 5, 6, 10, 13, 8, 1, 1, 2, 2, 2, 3, 5, 4, 2, 3, 5, 5, 6, 10, 13, 8, 2, 3, 5, 5, 6, 10, 13, 9, 6, 10, 14, 15, 21, 32, 33, 16, 1, 1, 2, 2, 2, 3, 5, 4, 2, 3, 5, 5, 6, 10, 13, 8, 2, 3, 5, 5
Offset: 1

Views

Author

Omar E. Pol, May 23 2009

Keywords

Comments

Row lengths are the terms of A000079 multiplied by 2. Right border gives A000079. - Omar E. Pol, Mar 19 2020

Examples

			From _Omar E. Pol_, Mar 19 2020: (Start)
Triangle begins:
  1,1;
  1,1,2,2;
  1,1,2,2,2,3,5,4;
  1,1,2,2,2,3,5,4,2,3,5,5,6,10,13,8;
  1,1,2,2,2,3,5,4,2,3,5,5,6,10,13,8,2,3,5,5,6,10,13,9,6,10,14,15,21,32,33,16;
  ... (End)

Links

Crossrefs

Cf. A139250, A139251, A160160, A160161, A160406, A160407, A160408, A160409.

Extensions

More terms from Jinyuan Wang, Mar 14 2020

A160728 Toothpick cube: a(n) = A160408(n)*6.

Original entry on oeis.org

0, 6, 12, 24, 48, 72, 96, 120, 144, 192, 288, 384, 432, 456, 480, 528
Offset: 0

Views

Author

Omar E. Pol, Jun 06 2009

Keywords

Comments

Also, 6 times the toothpick pyramid A160408.
The sequence gives the number of toothpicks after n rounds. A160729 (the first differences) gives the number added at the n-th round.
See also the entry A139250 for more information about the toothpick sequences.

Links

Crossrefs

Toothpick triangle: A160406. Toothpick pyramid: A160408.
Cf. A139250, A139251, A160160, A160729.

A162798 a(n) = A160161(n+1)/2.

Original entry on oeis.org

1, 2, 4, 4, 4, 4, 8, 16, 28, 16, 8, 4, 8, 16, 28, 28, 32, 40, 76, 116, 176, 72, 24, 16, 12, 20, 28, 28, 32, 40, 76, 116, 176, 108, 84, 88, 136, 180, 248, 224, 268, 332, 584, 744, 1000, 384, 152, 168, 132, 96, 56, 60, 64, 56, 84, 120, 176, 108, 84, 88, 136, 180, 248, 224
Offset: 1

Views

Author

Omar E. Pol, Jul 28 2009

Keywords

Links

Crossrefs

Cf. A139250, A139251, A160160, A160161, A162799.
Previous Showing 11-20 of 22 results. Next

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

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