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.

A194435 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A194434.

Original entry on oeis.org

0, 4, 8, 16, 16, 16, 32, 44, 32, 16, 32, 64, 96, 48, 80, 100, 64, 16, 32, 64, 96, 112, 144, 168, 176, 80, 96, 160, 256, 128, 176, 212, 128, 16, 32, 64, 96, 112, 144, 176, 208, 168, 192, 240, 400, 272, 336, 332, 336, 112, 96, 176, 288, 336, 416, 464
Offset: 0

Views

Author

Omar E. Pol, Sep 03 2011

Keywords

Comments

Essentially the first differences of A194434.
First differs from A221528 at a(13). - Omar E. Pol, Mar 23 2013
From Omar E. Pol, Jun 24 2022: (Start)
The word of this cellular automaton is "ab".
For the nonzero terms the structure of the irregular triangle is as shown below:
a,b;
a,b;
a,b,a,b;
a,b,a,b,a,b,a,b;
a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b;
...
Row lengths are the terms of A011782 multiplied by 2, also the column 2 of A296612.
Columns "a" contain numbers of D-toothpicks (of length sqrt(2)).
Columns "b" contain numbers of toothpicks (of length 1).
An associated sound to the animation could be (tick, tock), (tick, tock), ..., the same as the ticking clock sound.
For further information about the word of cellular automata see A296612. (End)

Examples

			From _Omar E. Pol_, Mar 23 2013: (Start)
When written as an irregular triangle the sequence of nonzeros terms begins:
   4, 8;
  16,16;
  16,32,44,32;
  16,32,64,96, 48, 80,100, 64;
  16,32,64,96,112,144,168,176, 80, 96,160,256,128,176,212,128;
  16,32,64,96,112,144,176,208,168,192,240,400,272,336,332,336,112,96, ...
  ... (End)
Right border gives the powers of 2 >= 8 (reformatted the triangle). - _Omar E. Pol_, Jun 24 2022

Links

Crossrefs

Cf. A011782, A139251, A194271, A194433, A194434, A194441, A194443, A194445, A212009, A221528, A299612.

Formula

a(n) = 4*A194445(n).
Conjecture: a(2^k+1) = 16, if k >= 1.

Extensions

More terms from Omar E. Pol, Mar 23 2013

A299609 Number of nX5 0..1 arrays with every element equal to 1, 2, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

3, 23, 23, 85, 179, 453, 1006, 2523, 6002, 14802, 36299, 87591, 214486, 522937, 1275628, 3120041, 7614933, 18586581, 45384416, 110821038, 270585507, 660827950, 1613737854, 3940683638, 9622959317, 23498981429, 57383159995, 140126697433
Offset: 1

Views

Author

R. H. Hardin, Feb 14 2018

Keywords

Comments

Column 5 of A299612.

Examples

			Some solutions for n=6
..0..1..0..0..0. .0..1..0..0..0. .0..1..1..0..1. .0..1..1..0..1
..0..0..1..1..1. .1..0..1..1..1. .1..0..0..0..1. .0..0..0..0..1
..0..0..0..0..0. .1..0..0..0..0. .1..0..0..0..1. .0..0..0..0..1
..1..0..0..0..1. .1..0..0..0..1. .0..0..0..0..0. .1..0..0..0..0
..1..0..0..0..1. .0..0..0..0..1. .0..0..1..1..1. .1..0..0..0..0
..1..0..1..1..0. .1..1..1..0..1. .0..1..0..0..0. .1..0..1..1..0

Links

Crossrefs

Cf. A299612.

A299610 Number of nX6 0..1 arrays with every element equal to 1, 2, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

5, 49, 34, 173, 453, 1223, 3286, 9873, 28227, 86428, 253623, 766882, 2299579, 6887900, 20699158, 62239664, 186995764, 562324870, 1690827365, 5083949541, 15289512249, 45981730995, 138278962826, 415872244403, 1250740118045
Offset: 1

Views

Author

R. H. Hardin, Feb 14 2018

Keywords

Comments

Column 6 of A299612.

Examples

			Some solutions for n=5
..0..1..0..0..0..1. .0..0..0..1..1..0. .0..0..0..1..1..0. .0..1..1..0..1..0
..0..1..1..1..1..0. .1..0..0..0..0..1. .1..0..0..0..0..1. .1..0..0..0..1..0
..0..1..1..1..0..1. .0..1..0..0..0..1. .0..1..0..0..0..1. .1..0..0..0..1..0
..1..1..1..1..0..1. .1..0..0..0..0..0. .0..1..0..0..0..0. .0..0..0..0..0..1
..0..0..0..1..0..1. .0..0..0..1..1..1. .0..1..0..1..1..1. .1..1..1..0..0..0

Links

Crossrefs

Cf. A299612.

A299611 Number of nX7 0..1 arrays with every element equal to 1, 2, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 95, 63, 322, 1006, 3286, 13490, 49047, 183585, 713699, 2714170, 10378456, 39704472, 151771262, 581376350, 2226003287, 8517881481, 32604243139, 124809117768, 477707469245, 1828508432121, 6999126323813, 26790197380901
Offset: 1

Views

Author

R. H. Hardin, Feb 14 2018

Keywords

Comments

Column 7 of A299612.

Examples

			Some solutions for n=5
..0..1..0..1..0..0..0. .0..0..0..1..1..1..0. .0..0..1..1..1..0..1
..0..1..0..1..1..1..1. .1..0..0..0..0..0..0. .1..1..0..0..0..0..1
..0..1..0..1..1..1..0. .1..0..0..0..0..1..1. .1..0..1..0..0..0..1
..1..1..1..1..1..1..0. .0..0..0..0..0..0..0. .0..0..0..0..0..0..0
..0..0..1..1..0..0..1. .1..1..1..0..0..1..1. .1..1..0..0..1..1..1

Links

Crossrefs

Cf. A299612.

A299608 Number of n X n 0..1 arrays with every element equal to 1, 2, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 3, 15, 40, 179, 1223, 13490, 231838, 6506278, 335604816
Offset: 1

Views

Author

R. H. Hardin, Feb 14 2018

Keywords

Comments

Diagonal of A299612.

Examples

			Some solutions for n=6
..0..1..1..0..0..0. .0..0..1..0..1..1. .0..0..1..0..1..0. .0..0..1..1..0..1
..0..0..0..0..0..1. .1..0..1..0..0..1. .1..0..1..0..1..0. .1..1..1..1..1..0
..0..0..0..0..0..1. .1..1..1..1..1..1. .1..0..0..0..0..1. .0..0..1..1..1..1
..1..0..0..0..0..0. .1..1..1..1..1..1. .0..1..0..0..0..0. .1..0..1..1..1..1
..1..0..0..1..0..0. .0..1..1..1..1..0. .0..1..0..0..0..0. .0..1..0..0..1..0
..1..0..1..0..1..0. .1..0..1..1..0..1. .0..1..0..1..1..0. .1..0..1..0..1..0

Crossrefs

Cf. A299612.
Showing 1-5 of 5 results.

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