

A266285


Number of ON (black) cells in the nth iteration of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell.


1



1, 1, 2, 4, 3, 7, 4, 10, 5, 13, 6, 16, 7, 19, 8, 22, 9, 25, 10, 28, 11, 31, 12, 34, 13, 37, 14, 40, 15, 43, 16, 46, 17, 49, 18, 52, 19, 55, 20, 58, 21, 61, 22, 64, 23, 67, 24, 70, 25, 73, 26, 76, 27, 79, 28, 82, 29, 85, 30, 88, 31, 91, 32, 94, 33, 97, 34
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OFFSET

0,3


REFERENCES

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


LINKS

Robert Price, Table of n, a(n) for n = 0..999
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Index entries for sequences related to cellular automata
Index to Elementary Cellular Automata


FORMULA

Conjectures from Colin Barker, Dec 28 2015 and Apr 14 2019: (Start)
a(n) = ((1)^n*(32*n)+4*n+1)/4.
a(n) = 2*a(n2)a(n4) for n>3.
G.f.: (1+x+2*x^3) / ((1x)^2*(1+x)^2).
(End)


MATHEMATICA

rule=13; 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. A266282.
Sequence in context: A007203 A354707 A110412 * A258851 A194031 A340245
Adjacent sequences: A266282 A266283 A266284 * A266286 A266287 A266288


KEYWORD

nonn,easy


AUTHOR

Robert Price, Dec 26 2015


EXTENSIONS

Conjectures from Colin Barker, Apr 14 2019


STATUS

approved



