A267058 Decimal representation of the n-th iteration of the "Rule 97" elementary cellular automaton starting with a single ON (black) cell.

1, 0, 20, 19, 256, 255, 5120, 5119, 65536, 65535, 1310720, 1310719, 16777216, 16777215, 335544320, 335544319, 4294967296, 4294967295, 85899345920, 85899345919, 1099511627776, 1099511627775, 21990232555520, 21990232555519, 281474976710656, 281474976710655

Offset

0,3

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

Conjectures from Colin Barker, Jan 10 2016 and Apr 19 2019: (Start)

a(n) = a(n-2)+256*a(n-4)-256*a(n-6) for n>5.

G.f.: (1+19*x^2+19*x^3-20*x^4+236*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1+16*x^2)).

(End)

Conjecture: a(n) = 256^floor(n/4)*(((n-1)/2 + 1) mod 2) + 20*256^floor(n/4)*(((n-1)/2) mod 2) - 1 for odd n; a(n) = 256^floor(n/4)*((n/2 + 1) mod 2) + 20*256^floor(n/4)*((n/2) mod 2) for even n. - Karl V. Keller, Jr., Jul 03 2022

Mathematica

rule=97; 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. A267056, A267057.

Sequence in context: A023462 A261307 A172164 * A205545 A087708 A220022

Adjacent sequences: A267055 A267056 A267057 * A267059 A267060 A267061

Keyword

nonn,easy

Author

Robert Price, Jan 09 2016

Status

approved