A267453 Number of OFF (white) cells in the n-th iteration of the "Rule 131" elementary cellular automaton starting with a single ON (black) cell.

0, 2, 3, 5, 5, 8, 7, 10, 11, 12, 12, 16, 15, 17, 18, 20, 20, 23, 22, 25, 26, 27, 27, 31, 30, 32, 33, 35, 35, 38, 37, 40, 41, 42, 42, 46, 45, 47, 48, 50, 50, 53, 52, 55, 56, 57, 57, 61, 60, 62, 63, 65, 65, 68, 67, 70, 71, 72, 72, 76, 75, 77, 78, 80, 80, 83

Offset

0,2

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 15 2016 and Apr 19 2019: (Start)

a(n) = a(n-3)+a(n-4)-a(n-7) for n>6.

G.f.: x*(2+3*x+5*x^2+3*x^3+3*x^4-x^5) / ((1-x)^2*(1+x)*(1+x^2)*(1+x+x^2)).

(End)

Mathematica

rule=131; 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 *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}] (* Number of White cells in stage n *)

Crossrefs

Cf. A267418.

Sequence in context: A158185 A095413 A134871 * A063914 A209187 A357259

Adjacent sequences: A267450 A267451 A267452 * A267454 A267455 A267456

Keyword

nonn,easy

Author

Robert Price, Jan 15 2016

Status

approved