A267255 Decimal representation of the n-th iteration of the "Rule 111" elementary cellular automaton starting with a single ON (black) cell.

1, 6, 7, 122, 31, 2018, 95, 32738, 95, 524258, 95, 8388578, 95, 134217698, 95, 2147483618, 95, 34359738338, 95, 549755813858, 95, 8796093022178, 95, 140737488355298, 95, 2251799813685218, 95, 36028797018963938, 95, 576460752303423458, 95, 9223372036854775778

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

From Colin Barker, Jan 13 2016 and Apr 19 2019: (Start)

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

G.f.: (1+6*x-10*x^2+20*x^3-72*x^4+40*x^5-320*x^6+384*x^7-1024*x^8) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).

(End)

a(n) = 2*4^n - 30 for odd n>4; a(n) = 95 for even n>4. - Karl V. Keller, Jr., Sep 12 2021

Mathematica

rule=111; 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 *)

Prog

(Python) print([1, 6, 7, 122, 31] + [2*4**n - 30 if n%2 else 95  for n in range(5, 50)]) # Karl V. Keller, Jr., Sep 12 2021

Crossrefs

Cf. A267253, A267254.

Sequence in context: A041081 A041082 A036417 * A041357 A041829 A042497

Adjacent sequences: A267252 A267253 A267254 * A267256 A267257 A267258

Keyword

nonn,easy

Author

Robert Price, Jan 12 2016

Status

approved