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A267360 Decimal representation of the n-th iteration of the "Rule 125" elementary cellular automaton starting with a single ON (black) cell. 2
1, 3, 28, 47, 496, 575, 8000, 9215, 128000, 147455, 2048000, 2359295, 32768000, 37748735, 524288000, 603979775, 8388608000, 9663676415, 134217728000, 154618822655, 2147483648000, 2473901162495, 34359738368000, 39582418599935, 549755813888000, 633318697598975 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Index entries for linear recurrences with constant coefficients, signature (0,17,0,-16).

FORMULA

Conjectures from Colin Barker, Jan 14 2016 and Apr 19 2019: (Start)

a(n) = 17*a(n-2)-16*a(n-4) for n>8.

G.f.: (1+3*x+11*x^2-4*x^3+36*x^4-176*x^5+16*x^6+192*x^7-64*x^8) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).

(End)

MATHEMATICA

rule=125; 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. A267358, A267359.

Sequence in context: A157848 A225674 A253653 * A046104 A116984 A229055

Adjacent sequences: A267357 A267358 A267359 * A267361 A267362 A267363

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 13 2016

EXTENSIONS

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022

STATUS

approved

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Last modified December 6 08:31 EST 2022. Contains 358605 sequences. (Running on oeis4.)