A266259 Total number of OFF (white) cells after n iterations of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell.

0, 2, 5, 7, 14, 16, 27, 29, 44, 46, 65, 67, 90, 92, 119, 121, 152, 154, 189, 191, 230, 232, 275, 277, 324, 326, 377, 379, 434, 436, 495, 497, 560, 562, 629, 631, 702, 704, 779, 781, 860, 862, 945, 947, 1034, 1036, 1127, 1129, 1224, 1226, 1325, 1327, 1430

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.: x*(2+3*x-2*x^2+x^3) / ((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 *) 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. A266253.

Sequence in context: A230301 A031457 A044990 * A133146 A217753 A022771

Adjacent sequences: A266256 A266257 A266258 * A266260 A266261 A266262

Keyword

nonn,easy

Author

Robert Price, Dec 25 2015

Extensions

Conjectures from Colin Barker, Apr 14 2019

Status

approved