A253086 Number of ON cells at generation n of 5-celled totalistic CA defined by Rule 780.

1, 4, 5, 12, 4, 16, 20, 48, 17, 24, 36, 80, 12, 48, 60, 144, 40, 56, 108, 200, 56, 72, 140, 200, 156, 176, 232, 368, 140, 232, 336, 440, 316, 304, 388, 544, 316, 344, 364, 464, 460, 424, 508, 584, 448, 488, 780, 808, 688, 624, 792, 1120, 736, 784, 860, 1240, 876, 1088, 1100

Offset: 0

Author

N. J. A. Sloane, Feb 11 2015

Keywords

• nonn

Comments

A minor observation: if written as an irregular triangle T(n,k), n>=1, k>=1, in which the row lengths are the powers of 2 greater than 2 we have that T(2,k) = 4*T(1,k) and T(3,k) = 12*T(1,k), but in both cases only for 1<=k<=4. - Omar E. Pol, Feb 14 2015

Equivalent to the following "Rules": 260,268,292,300,388,396,420,428,772,780,804,812,900,908,932,940. - Robert Price, Mar 30 2016

References

• S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..511
• N. J. A. Sloane, Illustration of generations 0-15
• N. J. A. Sloane, Illustration of generations 0-31
• N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168, 2015
• Index entries for sequences related to cellular automata
• Index to 2D 5-Neighbor Cellular Automata
• Index to Elementary Cellular Automata

Crossrefs

Cf. A246310 (8-neighbor analog), A253087.

Programs

Mathematica

Map[Function[Apply[Plus, Flatten[#1]]],
CellularAutomaton[{780, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 128]]
ArrayPlot /@
CellularAutomaton[{780, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 31]

Formula

It would be nice to have a recurrence.