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 21-25 of 25 results.

A255264 Total number of ON cells in the "Ulam-Warburton" two-dimensional cellular automaton of A147562 after A048645(n) generations.

Original entry on oeis.org

1, 5, 9, 21, 25, 37, 85, 89, 101, 149, 341, 345, 357, 405, 597, 1365, 1369, 1381, 1429, 1621, 2389, 5461, 5465, 5477, 5525, 5717, 6485, 9557, 21845, 21849, 21861, 21909, 22101, 22869, 25941, 38229, 87381, 87385, 87397, 87445, 87637
Offset: 1

Views

Author

Omar E. Pol, Feb 19 2015

Keywords

Comments

It appears that these are the terms of A147562, A162795, A169707, A255366, A256250, A256260, whose indices have binary weight 1 or 2.

Examples

			Also, written as an irregular triangle in which row lengths are the terms of A028310 the sequence begins:
      1;
      5;
      9,    21;
     25,    37,    85;
     89,   101,   149,   341;
    345,   357,   405,   597,  1365;
   1369,  1381,  1429,  1621,  2389,  5461;
   5465,  5477,  5525,  5717,  6485,  9557, 21845;
  21849, 21861, 21909, 22101, 22869, 25941, 38229, 87381;
  ...
Right border gives the positive terms of A002450.
It appears that the second leading diagonal gives the odd terms of A206374.

Links

Crossrefs

Cf. A002450, A028310, A032925, A048645, A075897, A139250, A147562, A162795, A169707, A206374, A209492, A255263, A255366, A256250, A256260.

Formula

a(n) = A147562(A048645(n)).
Conjecture 1: a(n) = A162795(A048645(n)).
Conjecture 2: a(n) = A169707(A048645(n)).
Conjecture 3: a(n) = A255366(A048645(n)).
Conjecture 4: a(n) = A256250(A048645(n)).
Conjecture 5: a(n) = A256260(A048645(n)).
a(n) = A032925(A209492(n-1)) (conjectured). - Jon Maiga, Dec 17 2021

A256138 Total number of ON states after n generations of cellular automaton of A151723 based on hexagons, if we only look at two opposite 120-degree wedges, including the central cell.

Original entry on oeis.org

1, 5, 9, 21, 25, 37, 57, 85, 89, 101, 121, 157, 193, 221, 273, 333, 337, 349, 369, 405, 441, 477, 545, 645, 713, 741, 793, 885, 993, 1069, 1193, 1317, 1321, 1333, 1353, 1389, 1425, 1461, 1529, 1629, 1697, 1733, 1801, 1917, 2065, 2197, 2361, 2589, 2721, 2749, 2801, 2893, 3001, 3109, 3281, 3549, 3785, 3893, 4017, 4237, 4513, 4709, 4985, 5237
Offset: 1

Views

Author

Omar E. Pol, Mar 20 2015

Keywords

Comments

First differs from both A169707 and A246335 at a(12).
First differs from the average of A169707 and A246335 at a(13).
Note that the above mentioned cellular automata work on the square grid.
A256139 gives the number of cells turned ON at the n-th stage.

Links

Crossrefs

Cf. A151723, A169707, A169779, A169780, A170898, A246333, A246335, A256139.

Formula

a(n) = 1 + 2*(A151723(n) - 1)/3 = 1 - 4*n + 4*A169780(n).
a(n) = 1 + 4*A169779(n-2), n >= 2.
a(n) = A151723(n) - 2*A169779(n-2), n >= 2.

A255049 a(n) = 2*A160552(n).

Original entry on oeis.org

0, 2, 2, 6, 2, 6, 10, 14, 2, 6, 10, 14, 10, 22, 34, 30, 2, 6, 10, 14, 10, 22, 34, 30, 10, 22, 34, 38, 42, 78, 98, 62, 2, 6, 10, 14, 10, 22, 34, 30, 10, 22, 34, 38, 42, 78, 98, 62, 10, 22, 34, 38, 42, 78, 98, 70, 42, 78, 106, 118, 162, 254, 258, 126, 2, 6, 10, 14, 10
Offset: 0

Views

Author

Omar E. Pol, Feb 13 2015

Keywords

Examples

			Written as an irregular triangle in which row lengths are the terms of A011782 the sequence begins:
0;
2;
2,6;
2,6,10,14;
2,6,10,14,10,22,34,30;
2,6,10,14,10,22,34,30,10,22,34,38,42,78,98,62;
2,6,10,14,10,22,34,30,10,22,34,38,42,78,98,62,10,22,34,38,42,78,98,70,42,78,106,118,162,254,258,126;
It appears that row sums give 0 together with A004171, (see also A081294).
It appears that right border gives the nonnegative terms of A000918, (see also A095121).

Links

Crossrefs

Cf. A000918, A004171, A081294, A095121, A139250, A160164, A160552, A169707, A169708, A187220.

Formula

It appears that a(n) = A169708(n)/2, n >= 1.

Extensions

Edited by Omar E. Pol, Feb 18 2015

A255166 Difference after n generations between the total number of single toothpicks in the I-toothpick structure of A160164 and the total number of ON cells in the "Ulam-Warburton" two-dimensional cellular automaton of A147562.

Original entry on oeis.org

0, 1, 1, 5, 1, 5, 9, 21, 1, 5, 9, 21, 9, 29, 49, 77, 1, 5, 9, 21, 9, 29, 49, 77, 9, 29, 49, 85, 57, 141, 209, 261, 1, 5, 9, 21, 9, 29, 49, 77, 9, 29, 49, 85, 57, 141, 209, 261, 9, 29, 49, 85, 57, 141, 209, 269, 57, 141, 217, 333, 289, 597, 785, 845, 1, 5, 9, 21, 9, 29, 49, 77, 9, 29, 49, 85, 57, 141, 209, 261, 9, 29, 49, 85
Offset: 0

Views

Author

Omar E. Pol, Feb 15 2015

Keywords

Examples

			Written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:
0;
1;
1,5;
1,5,9,21;
1,5,9,21,9,29,49,77;
1,5,9,21,9,29,49,77,9,29,49,85,57,141,209,261;
1,5,9,21,9,29,49,77,9,29,49,85,57,141,209,261,9,29,49,85,57,141,209,269,57,141,217,333,289,597,785,845;
...
It appears that the right border gives [0, 1] together with A126645. The right border gives the largest difference between both C.A. in every period.
Also, written the positive terms as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:
1;
1;
5,1;
5,9,21,1;
5,9,21,9,29,49,77,1;
5,9,21,9,29,49,77,9,29,49,85,57,141,209,261,1;
5,9,21,9,29,49,77,9,29,49,85,57,141,209,261,9,29,49,85,57,141,209,269,57,141,217,333,289,597,785,845,1;
...
The right border gives A000012 according with the illustrations as shown below. In this triangle the right border gives the smallest difference between both C.A. in every period.
For example: after 8 generations the structures look like this:
.
.                                      O
.                                    O O O
.                                  O   O   O
.    _ _ _ _ _ _ _ _             O O O O O O O
.     |_ _|   |_ _|            O   O   O   O   O
.     | |_|_ _|_| |          O O O   O O O   O O O
      |_|_|_ _|_|_|        O   O   O   O   O   O   O
.     |   | | |   |      O O O O O O O O O O O O O O O
.     |_ _|_|_|_ _|        O   O   O   O   O   O   O
.     | |_|_ _|_| |          O O O   O O O   O O O
.     |_|_|   |_|_|            O   O   O   O   O
.    _|_ _|_ _|_ _|_             O O O O O O O
.                                  O   O   O
.     86 toothpicks                  O O O
.                                      O
.
.                                 85 ON cells
.
a(8) = 1 because the I-toothpick structure contains 86 single toothpicks and the "Ulam-Warburton" two-dimensional cellular automaton has 85 ON cells, so the difference of the number of elements between both structures is equal to 86 - 85 = 1.

Links

Crossrefs

Cf. A126645, A139250, A147562, A160164, A169707, A170903.

Formula

a(n) = A160164(n) - A147562(n).

A288775 Difference between the total number of toothpicks in the toothpick structure of A139250 that are parallel to the initial toothpick after n odd stages, and the total number of "ON" cells at n-th stage in the "Ulam-Warburton" two-dimensional cellular automaton of A147562.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 4, 28, 0, 0, 0, 4, 0, 4, 4, 28, 0, 4, 4, 28, 4, 28, 32, 132, 0, 0, 0, 4, 0, 4, 4, 28, 0, 4, 4, 28, 4, 28, 32, 132, 0, 4, 4, 28, 4, 28, 32, 132, 4, 28, 32, 132, 32, 136, 176, 524, 0, 0, 0, 4, 0, 4, 4, 28, 0, 4, 4, 28, 4, 28, 32, 132, 0, 4, 4, 28, 4, 28, 32, 132, 4, 28, 32
Offset: 1

Views

Author

Omar E. Pol, Jul 04 2017

Keywords

Comments

It appears that a(n) = 0 if and only if n is a member of A048645.
First differs from A255263 at a(14), with which it shares infinitely many terms.
It appears that A147562(n) = A162795(n) = A169707(n) = A255366(n) = A256250(n) = A256260(n), if n is a member of A048645.

Examples

			Written as an irregular triangle T(j,k), k>=1, in which the row lengths are the terms of A011782, the sequence begins:
0;
0;
0,0;
0,0,4,0;
0,0,4,0,4,4,28,0;
0,0,4,0,4,4,28,0,4,4,28,4,28,32,132,0;
0,0,4,0,4,4,28,0,4,4,28,4,28,32,132,0,4,4,28,4,28,32,132,4,28,32,132,32,136,176,524,0;
...
It appears that if k is a power of 2 then T(j,k) = 0.
It appears that every column lists the same terms as its initial term.

Links

Crossrefs

Cf. A011782, A048645, A139250, A139251, A147562, A147582, A162793, A162795, A169707, A255263, A255366, A256250, A256260.

Formula

a(n) = A162795(n) - A147562(n).
Previous Showing 21-25 of 25 results.

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

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