A266304 Total number of OFF (white) cells after n iterations of the "Rule 15" elementary cellular automaton starting with a single ON (black) cell.

0, 1, 5, 6, 14, 15, 27, 28, 44, 45, 65, 66, 90, 91, 119, 120, 152, 153, 189, 190, 230, 231, 275, 276, 324, 325, 377, 378, 434, 435, 495, 496, 560, 561, 629, 630, 702, 703, 779, 780, 860, 861, 945, 946, 1034, 1035, 1127, 1128, 1224, 1225, 1325, 1326, 1430

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..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 28 2015 and Apr 15 2019: (Start)

a(n) = n*(n+(-1)^n+2)/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*(1+4*x-x^2) / ((1-x)^3*(1+x)^2). (End)

a(n) = Sum_{i=1..n} (n-i-1) mod 2. - Wesley Ivan Hurt, Sep 15 2017

Mathematica

rule=15; 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. A266300.

Sequence in context: A084381 A289895 A335785 * A359329 A308839 A099330

Adjacent sequences: A266301 A266302 A266303 * A266305 A266306 A266307

Keyword

nonn,easy

Author

Robert Price, Dec 26 2015

Status

approved