A262862 Decimal representation of the n-th iteration of the "Rule 147" elementary cellular automaton starting with a single ON (black) cell.

1, 5, 17, 93, 273, 1501, 4369, 24029, 69905, 384477, 1118481, 6151645, 17895697, 98426333, 286331153, 1574821341, 4581298449, 25197141469, 73300775185, 403154263517, 1172812402961, 6450468216285, 18764998447377, 103207491460573, 300239975158033

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 (0,17,0,-16).

Formula

From Colin Barker, Jan 17 2016 and Apr 17 2019: (Start)

a(n) = 17*a(n-2) - 16*a(n-4) for n>3.

G.f.: (1+5*x+8*x^3) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).

(End)

a(n) = floor((16 + 6*(n mod 2))*4^n / 15). - Karl V. Keller, Jr., Apr 14 2021

Mathematica

rule=147; 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([(16 + 6*(n%2))*4**n//15 for n in range(50)]) # Karl V. Keller, Jr., Apr 14 2021

Crossrefs

Cf. A262808.

Sequence in context: A197875 A203116 A198090 * A367921 A180382 A250717

Adjacent sequences: A262859 A262860 A262861 * A262863 A262864 A262865

Keyword

nonn,easy

Author

Robert Price, Jan 17 2016

Status

approved