A266436 Decimal representation of the n-th iteration of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell.

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

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