A266516 Decimal representation of the n-th iteration of the "Rule 29" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 4, 111, 16, 1983, 64, 32511, 256, 523263, 1024, 8384511, 4096, 134201343, 16384, 2147418111, 65536, 34359476223, 262144, 549754765311, 1048576, 8796088827903, 4194304, 140737471578111, 16777216, 2251799746576383, 67108864, 36028796750528511, 268435456

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 (0,21,0,-84,0,64).

Formula

Empirical a(n) = 21*a(n-2) - 84*a(n-4) + 64*a(n-6) for n>5. - Vincenzo Librandi, Dec 31 2015 and Apr 16 2019

Empirical g.f.: (1+3*x-17*x^2+48*x^3+16*x^4-96*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)). - Colin Barker, Dec 31 2015 and Apr 16 2019

Conjecture: a(n) = 2*(4^n - 2^n) - 1 for odd n; a(n) = 2^n for even n. - Karl V. Keller, Jr., Oct 03 2021

Mathematica

rule=29; 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. A266514, A266515.

Sequence in context: A126578 A332972 A041351 * A066496 A041465 A004124

Adjacent sequences: A266513 A266514 A266515 * A266517 A266518 A266519

Keyword

nonn,easy

Author

Robert Price, Dec 30 2015

Status

approved