A267454 Total number of OFF (white) cells after n iterations of the "Rule 131" elementary cellular automaton starting with a single ON (black) cell.

0, 2, 5, 10, 15, 23, 30, 40, 51, 63, 75, 91, 106, 123, 141, 161, 181, 204, 226, 251, 277, 304, 331, 362, 392, 424, 457, 492, 527, 565, 602, 642, 683, 725, 767, 813, 858, 905, 953, 1003, 1053, 1106, 1158, 1213, 1269, 1326, 1383, 1444, 1504, 1566, 1629, 1694

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-1)+a(n-3)-a(n-5)-a(n-7)+a(n-8) for n>7.

G.f.: x*(2+3*x+5*x^2+3*x^3+3*x^4-x^5) / ((1-x)^3*(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 *) nwc=Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc, k]], {k, 1, rows}] (* Number of White cells through stage n *)

Crossrefs

Cf. A267418.

Sequence in context: A080551 A179207 A008822 * A013927 A163059 A099738

Adjacent sequences: A267451 A267452 A267453 * A267455 A267456 A267457

Keyword

nonn,easy

Author

Robert Price, Jan 15 2016

Status

approved