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A266793 Total number of ON (black) cells after n iterations of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell. 1
1, 3, 5, 10, 14, 21, 26, 37, 42, 57, 62, 81, 86, 109, 114, 141, 146, 177, 182, 217, 222, 261, 266, 309, 314, 361, 366, 417, 422, 477, 482, 541, 546, 609, 614, 681, 686, 757, 762, 837, 842, 921, 926, 1009, 1014, 1101, 1106, 1197, 1202, 1297, 1302, 1401, 1406 (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, Jan 04 2016 and Apr 18 2019: (Start)

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

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>8.

G.f.: (1+2*x+x^3+x^4-x^5-x^6+2*x^7-x^8) / ((1-x)^3*(1+x)^2).

(End)

MATHEMATICA

rule=61; 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. A266786.

Sequence in context: A195094 A308805 A001841 * A176222 A008610 A281688

Adjacent sequences:  A266790 A266791 A266792 * A266794 A266795 A266796

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 03 2016

STATUS

approved

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Last modified June 21 01:12 EDT 2021. Contains 345339 sequences. (Running on oeis4.)