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A266436 Decimal representation of the n-th iteration of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell. 3
1, 7, 0, 127, 0, 2047, 0, 32767, 0, 524287, 0, 8388607, 0, 134217727, 0, 2147483647, 0, 34359738367, 0, 549755813887, 0, 8796093022207, 0, 140737488355327, 0, 2251799813685247, 0, 36028797018963967, 0, 576460752303423487, 0, 9223372036854775807, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

With the exception of a(1) the same as A266380, A266324 and A266218. - R. J. Mathar, Jan 10 2016

LINKS

Robert Price, Table of n, a(n) for n = 0..500

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, Dec 30 2015 and Apr 15 2019: (Start)

a(n) = ((-1)^n+2^(2*n+1)-(-1)^n*2^(2*n+1)-1)/2 for n>0.

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

G.f.: (1+7*x-17*x^2+8*x^3+16*x^4) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).

(End)

a(n) = (2*4^n-1)*(n mod 2) + 0^n. - Karl V. Keller, Jr., Jul 06 2021

MATHEMATICA

rule=23; 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([(2*4**n-1)*(n%2) + 0**n for n in range(33)]) # Karl V. Keller, Jr., Jul 06 2021

CROSSREFS

Cf. A241955, A266434, A266435 (binary).

Sequence in context: A352078 A046273 A167317 * A240822 A240810 A024094

Adjacent sequences: A266433 A266434 A266435 * A266437 A266438 A266439

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 29 2015

STATUS

approved

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Last modified December 9 19:36 EST 2022. Contains 358703 sequences. (Running on oeis4.)