A266450 Total number of OFF (white) cells after n iterations of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.

0, 2, 5, 9, 14, 19, 28, 33, 46, 51, 68, 73, 94, 99, 124, 129, 158, 163, 196, 201, 238, 243, 284, 289, 334, 339, 388, 393, 446, 451, 508, 513, 574, 579, 644, 649, 718, 723, 796, 801, 878, 883, 964, 969, 1054, 1059, 1148, 1153, 1246, 1251, 1348, 1353, 1454

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..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, Dec 31 2015 and Apr 16 2019: (Start)

a(n) = (2*n^2+2*((-1)^n+3)*n-7*(-1)^n-1)/4 for n>2.

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

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

(End)

Mathematica

rule=25; 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. A266441.

Sequence in context: A024201 A110443 A130029 * A361742 A132296 A275586

Adjacent sequences: A266447 A266448 A266449 * A266451 A266452 A266453

Keyword

nonn,easy

Author

Robert Price, Dec 29 2015

Status

approved