

A267872


Number of ON (black) cells in the nth 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(n1)a(n2) for n>3.
G.f.: (1x+4*x^22*x^3) / (1x)^2.
(End)


MATHEMATICA

rule=237; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rowsk+1, rows+k1}], {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



