A151836 -id:A151836 - cp's OEIS frontend

A151837 a(n) = A151836(n)/4.

1, 1, 3, 1, 3, 3, 7, 1, 3, 3, 7, 5, 7, 9, 17, 1, 3, 3, 7, 5, 7, 9, 17, 9, 7, 9, 17, 17, 19, 25, 43, 3, 7, 3, 7, 5, 7, 9, 17, 9, 7, 9, 17, 17, 19, 25, 43, 19, 7, 9, 17, 17, 19, 25, 43, 35, 23, 25, 43, 51, 55, 69, 113, 15, 23, 3, 7, 5, 7, 9, 17, 9, 7, 9, 17, 17

Offset: 2

N. J. A. Sloane, Jul 13 2009

nonn

Rémy Sigrist, Table of n, a(n) for n = 2..1023
Rémy Sigrist, C++ program for A151837

Cf. A151836.

More terms from Rémy Sigrist, Jan 08 2022

A151776 Number of ON states after n generations of cellular automaton based on f.c.c. lattice with each cell adjacent to its twelve neighbors.

Original entry on oeis.org

0, 1, 13, 25, 109, 121, 205, 385, 805, 817, 901, 1081, 1645, 2185, 2605, 3721, 5749, 5857, 5941, 6121, 6685, 7225, 7789, 9289, 12565, 14401, 14821, 15937, 18877, 23257, 25981, 32233, 42445, 43729, 44101, 44521

Offset: 0

N. J. A. Sloane, Jun 24 2009

nonn

We take the f.c.c. lattice to consist of the points (X,Y,Z) of Z^3 with X+Y+Z even.
We start with a single ON cell at the origin.
A cell is turned ON if exactly one of its twelve neighbors is ON. An ON cell remains ON forever.
Analog of A147562, which is corresponding sequence for the square lattice Z^2.
If we just look at what happens in the (X,Y)-plane, we get A147552 and A151836.

Nathaniel Johnston, Table of n, a(n) for n = 0..68
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
Nathaniel Johnston, C script
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Index entries for sequences related to f.c.c. lattice

Cf. A151777, A151778, A147562, A151725, A139250.

Terms after a(30) from Nathaniel Johnston, Mar 27 2011

A147552 Consider the cellular automaton based on the f.c.c. lattice described in A151776; sequence gives number of ON cells in generation n that lie in the (x,y) plane.

Original entry on oeis.org

0, 1, 5, 9, 21, 25, 37, 49, 77, 81, 93, 105, 133, 153, 181, 217, 285, 289, 301, 313, 341, 361, 389, 425, 493, 529, 557, 593, 661, 729, 805, 905, 1077, 1089, 1117, 1129, 1157, 1177, 1205, 1241, 1309, 1345, 1373, 1409, 1477, 1545, 1621, 1721, 1893, 1969, 1997, 2033

Offset: 0

N. J. A. Sloane, Jul 13 2009

nonn

First differs from A160720 at a(13).

Rémy Sigrist, Table of n, a(n) for n = 0..1023 (first 69 terms from Nathaniel Johnston)
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
Nathaniel Johnston, C script
Rémy Sigrist, Interactive scatterplot of the cells turned ON at generation 129 [provided your web browser supports the Plotly library, you should see icons on the top right corner of the page: if you choose "Orbital rotation", then you will be able to rotate the plot alongside three axes]
Rémy Sigrist, C++ program for A147552
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Cf. A151776, A151836 (first differences), A139250.

Terms after a(30) from Nathaniel Johnston, Mar 27 2011

cp's OEIS Frontend

A151837 a(n) = A151836(n)/4.

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A151776 Number of ON states after n generations of cellular automaton based on f.c.c. lattice with each cell adjacent to its twelve neighbors.

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Author

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Links

Crossrefs

Extensions

A147552 Consider the cellular automaton based on the f.c.c. lattice described in A151776; sequence gives number of ON cells in generation n that lie in the (x,y) plane.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions