A269543 Partial Sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 630", based on the 5-celled von Neumann neighborhood.

1, 6, 15, 36, 65, 110, 175, 264, 389, 522, 683, 864, 1077, 1338, 1615, 1948, 2293, 2786, 3307, 3880, 4457, 5110, 5783, 6568, 7377, 8282, 9291, 10324, 11321, 12522, 13715, 15072, 16461, 18202, 19763, 21628, 23441, 25454, 27443, 29664, 31821, 34178, 36571

Offset

0,2

Comments

Initialized with a single black (ON) cell at stage zero.

References

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

Links

Table of n, a(n) for n=0..42.

N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168, 2015

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to 2D 5-Neighbor Cellular Automata

Index to Elementary Cellular Automata

Mathematica

rule=630; stages=300; ca=CellularAutomaton[ {rule, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, stages]; (* Start with single black cell *) on=Map[Function[Apply[Plus, Flatten[#1]]], ca]; (* Count ON cells at each stage *) Table[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}]

Crossrefs

Cf. A269523.

Sequence in context: A273741 A273861 A074132 * A074149 A273411 A273490

Adjacent sequences: A269540 A269541 A269542 * A269544 A269545 A269546

Keyword

nonn,easy

Author

Robert Price, Mar 01 2016

Status

approved