A266590 Decimal representation of the n-th iteration of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 14, 65, 56, 1799, 224, 31775, 896, 520319, 3584, 8372735, 14336, 134154239, 57344, 2147229695, 229376, 34358722559, 917504, 549751750655, 3670016, 8796076769279, 14680064, 140737423343615, 58720256, 2251799553638399, 234881024, 36028795978776575

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

Formula

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

a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>7.

G.f.: (1+2*x-7*x^2+23*x^3-154*x^4+602*x^5+160*x^6-672*x^7) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).

(End)

Conjecture: a(n) = 2*4^n - 31*2^(n-2) - 1 for odd n > 1; a(n) = 7*2^(n-1) for even n > 1. - Karl V. Keller, Jr., Oct 06 2021

Mathematica

rule=37; 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. A266588, A266589.

Sequence in context: A222445 A181394 A335630 * A196977 A254197 A222715

Adjacent sequences: A266587 A266588 A266589 * A266591 A266592 A266593

Keyword

nonn,easy

Author

Robert Price, Jan 01 2016

Status

approved