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A266302 Decimal representation of the n-th iteration of the "Rule 15" elementary cellular automaton starting with a single ON (black) cell. 1
1, 6, 1, 126, 1, 2046, 1, 32766, 1, 524286, 1, 8388606, 1, 134217726, 1, 2147483646, 1, 34359738366, 1, 549755813886, 1, 8796093022206, 1, 140737488355326, 1, 2251799813685246, 1, 36028797018963966, 1, 576460752303423486, 1, 9223372036854775806, 1 (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..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) = (3*(-1)^n+2^(2*n+1)-(-1)^n*2^(2*n+1)-1)/2.

a(n) = 17*a(n-2)-16*a(n-4) for n>3.

G.f.: (1+6*x-16*x^2+24*x^3) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).

(End)

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 *) Table[FromDigits[catri[[k]], 2], {k, 1, rows}]   (* Decimal Representation of Rows *)

CROSSREFS

Cf. A266300.

Sequence in context: A318107 A331557 A303675 * A183284 A224476 A123147

Adjacent sequences:  A266299 A266300 A266301 * A266303 A266304 A266305

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 26 2015

STATUS

approved

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Last modified August 12 11:57 EDT 2020. Contains 336439 sequences. (Running on oeis4.)