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A267872 Number of ON (black) cells in the n-th iteration of the "Rule 237" elementary cellular automaton starting with a single ON (black) cell. 1
1, 1, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = A247328(n+1) for 2 <= n < 472, but a(472) = 945 differs from A247328(473) = 947. Furthermore, a(n) = A163985(n+1) for 2 <= n <= 1000. - Georg Fischer, Oct 22 2018

REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

LINKS

Robert Price, Table of n, a(n) for n = 0..1000

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 Elementary Cellular Automata

FORMULA

Conjectures from Colin Barker, Jan 22 2016 and Apr 20 2019: (Start)

a(n) = 2*a(n-1)-a(n-2) for n>3.

G.f.: (1-x+4*x^2-2*x^3) / (1-x)^2.

(End)

MATHEMATICA

rule=237; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Table[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)

CROSSREFS

Cf. A163985, A267870.

Sequence in context: A174392 A084926 A049013 * A062545 A020735 A329391

Adjacent sequences:  A267869 A267870 A267871 * A267873 A267874 A267875

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 21 2016

STATUS

approved

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Last modified January 19 17:59 EST 2020. Contains 331051 sequences. (Running on oeis4.)