A266257 Total number of ON (black) cells after n iterations of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 4, 9, 11, 20, 22, 35, 37, 54, 56, 77, 79, 104, 106, 135, 137, 170, 172, 209, 211, 252, 254, 299, 301, 350, 352, 405, 407, 464, 466, 527, 529, 594, 596, 665, 667, 740, 742, 819, 821, 902, 904, 989, 991, 1080, 1082, 1175, 1177, 1274, 1276, 1377, 1379

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..999

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

Conjectures from Colin Barker, Dec 27 2015 and Apr 14 2019: (Start)

a(n) = ((n+1)^2-(-1)^n*(n-1))/2.

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

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

(End)

Mathematica

rule=11; 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. A266253.

Sequence in context: A047348 A186699 A093859 * A115905 A292769 A307997

Adjacent sequences: A266254 A266255 A266256 * A266258 A266259 A266260

Keyword

nonn,easy

Author

Robert Price, Dec 25 2015

Extensions

Conjectures from Colin Barker, Apr 14 2019

Status

approved