A266813 Total number of OFF (white) cells after n iterations of the "Rule 62" elementary cellular automaton starting with a single ON (black) cell.

0, 0, 2, 3, 7, 10, 14, 19, 26, 31, 39, 47, 56, 65, 76, 86, 99, 111, 124, 138, 154, 168, 185, 202, 220, 238, 258, 277, 299, 320, 342, 365, 390, 413, 439, 465, 492, 519, 548, 576, 607, 637, 668, 700, 734, 766, 801, 836, 872, 908, 946, 983, 1023, 1062, 1102

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

Index entries for linear recurrences with constant coefficients, signature (1,0,1,0,-1,0,-1,1).

Formula

From Colin Barker, Jan 04 2016 and Apr 17 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*(2+x+4*x^2+x^3+x^4) / ((1-x)^3*(1+x)*(1+x^2)*(1+x+x^2)).

(End)

Mathematica

rule=62; 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. A071031, A266811 (total OFF cells).

Partial sums of A071046.

Sequence in context: A002238 A002255 A272649 * A344232 A370639 A361859

Adjacent sequences: A266810 A266811 A266812 * A266814 A266815 A266816

Keyword

nonn,easy

Author

Robert Price, Jan 03 2016

Status

approved