A266615 Total number of ON (black) cells after n iterations of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.

1, 1, 3, 6, 7, 15, 17, 28, 29, 45, 47, 66, 67, 91, 93, 120, 121, 153, 155, 190, 191, 231, 233, 276, 277, 325, 327, 378, 379, 435, 437, 496, 497, 561, 563, 630, 631, 703, 705, 780, 781, 861, 863, 946, 947, 1035, 1037, 1128, 1129, 1225, 1227, 1326, 1327, 1431

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 02 2016 and Apr 18 2019: (Start)

a(n) = a(n-1)+a(n-2)-a(n-3)+a(n-4)-a(n-5)-a(n-6)+a(n-7) for n>6.

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

(End)

Mathematica

rule=41; 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[Total[Take[nbc, k]], {k, 1, rows}] (* Number of Black cells through stage n *)

Crossrefs

Cf. A266608.

Sequence in context: A139247 A124611 A281900 * A043305 A227723 A192124

Adjacent sequences: A266612 A266613 A266614 * A266616 A266617 A266618

Keyword

nonn,easy

Author

Robert Price, Jan 01 2016

Status

approved