

A267360


Decimal representation of the nth 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
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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(n2)16*a(n4) for n>8.
G.f.: (1+3*x+11*x^24*x^3+36*x^4176*x^5+16*x^6+192*x^764*x^8) / ((1x)*(1+x)*(14*x)*(1+4*x)).
(End)


MATHEMATICA

rule=125; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rowsk+1, rows+k1}], {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



