A266245 Decimal representation of the n-th iteration of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.

1, 0, 5, 96, 29, 1952, 29, 32672, 29, 524192, 29, 8388512, 29, 134217632, 29, 2147483552, 29, 34359738272, 29, 549755813792, 29, 8796093022112, 29, 140737488355232, 29, 2251799813685152, 29, 36028797018963872, 29, 576460752303423392, 29, 9223372036854775712

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..999

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

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, Dec 28 2015 and Apr 14 2019: (Start)

a(n) = 17*a(n-2)-16*a(n-4) for n>7.

G.f.: (1-12*x^2+96*x^3-40*x^4+320*x^5-384*x^6+1024*x^7) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).

(End)

a(n) = 4^n/2 + 90*floor(4^n/60) - 90 for odd n>3; a(n) = 29 for even n>3. - Karl V. Keller, Jr., Aug 17 2021

Mathematica

rule=9; 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([1, 0, 5, 96]+[4**n//2 + 90*(4**n//60) - 90 if n%2 else 29 for n in range(4, 50)]) # Karl V. Keller, Jr., Aug 17 2021

Crossrefs

Cf. A266243, A266244.

Sequence in context: A218463 A192343 A152839 * A194616 A285367 A208253

Adjacent sequences: A266242 A266243 A266244 * A266246 A266247 A266248

Keyword

nonn,easy

Author

Robert Price, Dec 25 2015

Status

approved