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A267159 Total number of ON (black) cells after n iterations of the "Rule 107" elementary cellular automaton starting with a single ON (black) cell. 1
1, 2, 5, 10, 16, 24, 31, 44, 50, 65, 73, 94, 100, 123, 131, 160, 166, 197, 205, 242, 248, 287, 295, 340, 346, 393, 401, 454, 460, 515, 523, 584, 590, 653, 661, 730, 736, 807, 815, 892, 898, 977, 985, 1070, 1076, 1163, 1171, 1264, 1270, 1365, 1373, 1474, 1480 (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 11 2016 and Apr 19 2019: (Start)

a(n) = a(n-1)+a(n-2)-a(n-3)+a(n-4)-a(n-5)-a(n-6)+a(n-7) for n>12.

G.f.: (1+x+2*x^2+4*x^3+2*x^4+2*x^5-x^6+x^7-4*x^8-x^9+x^10+x^11-x^12) / ((1-x)^3*(1+x)^2*(1+x^2)).

(End)

MATHEMATICA

rule=107; 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. A267152.

Sequence in context: A131938 A031871 A026056 * A084587 A001859 A011903

Adjacent sequences:  A267156 A267157 A267158 * A267160 A267161 A267162

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 11 2016

STATUS

approved

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Last modified November 18 22:50 EST 2019. Contains 329305 sequences. (Running on oeis4.)