A266285 Number of ON (black) cells in the n-th iteration of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell.

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

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*(3-2*n)+4*n+1)/4.

a(n) = 2*a(n-2)-a(n-4) for n>3.

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

(End)

Mathematica

rule=13; 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. 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