A266610 Decimal representation of the n-th iteration of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.

1, 0, 5, 100, 1, 2040, 5, 32740, 1, 524280, 5, 8388580, 1, 134217720, 5, 2147483620, 1, 34359738360, 5, 549755813860, 1, 8796093022200, 5, 140737488355300, 1, 2251799813685240, 5, 36028797018963940, 1, 576460752303423480, 5, 9223372036854775780, 1

Offset

0,3

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

Formula

Conjectures from Colin Barker, Jan 02 2016 and Apr 18 2019: (Start)

a(n) = 16*a(n-2)+a(n-4)-16*a(n-6) for n>5.

G.f.: (1-11*x^2+100*x^3-80*x^4+440*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1+x^2)).

(End)

Conjecture: a(n) = 2*4^n + 2 - 10*(n mod 4) for odd n; a(n) = 5^((n mod 4)/2) for even n. - Karl V. Keller, Jr., Oct 07 2021

Mathematica

rule=41; 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. A266608, A266609.

Sequence in context: A277418 A318061 A147539 * A156276 A322715 A208348

Adjacent sequences: A266607 A266608 A266609 * A266611 A266612 A266613

Keyword

nonn,easy

Author

Robert Price, Jan 01 2016

Status

approved