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.

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

0,4

Links

Table of n, a(n) for n=0..83.

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for sequences related to cellular automata

Formula

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

Example

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.

Crossrefs

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

Sequence in context: A340213 A170903 A319663 * A131113 A139426 A143384

Adjacent sequences: A255163 A255164 A255165 * A255167 A255168 A255169

Keyword

nonn,tabf

Author

Omar E. Pol, Feb 15 2015

Status

approved