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A266450 Total number of OFF (white) cells after n iterations of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A132296 A275586 A075543

Adjacent sequences:  A266447 A266448 A266449 * A266451 A266452 A266453

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 29 2015

STATUS

approved

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Last modified August 25 03:10 EDT 2019. Contains 326318 sequences. (Running on oeis4.)