A267451 Number of ON (black) cells in the n-th iteration of the "Rule 131" elementary cellular automaton starting with a single ON (black) cell.

1, 1, 2, 2, 4, 3, 6, 5, 6, 7, 9, 7, 10, 10, 11, 11, 13, 12, 15, 14, 15, 16, 18, 16, 19, 19, 20, 20, 22, 21, 24, 23, 24, 25, 27, 25, 28, 28, 29, 29, 31, 30, 33, 32, 33, 34, 36, 34, 37, 37, 38, 38, 40, 39, 42, 41, 42, 43, 45, 43, 46, 46, 47, 47, 49, 48, 51, 50

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..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.: (1+x+2*x^2+x^3+2*x^4+2*x^6) / ((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 *) Table[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)

Crossrefs

Cf. A267418.

Sequence in context: A352956 A304214 A060367 * A062968 A239966 A341465

Adjacent sequences: A267448 A267449 A267450 * A267452 A267453 A267454

Keyword

nonn

Author

Robert Price, Jan 15 2016

Status

approved