A266218 Decimal representation of the n-th iteration of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.

1, 6, 0, 127, 0, 2047, 0, 32767, 0, 524287, 0, 8388607, 0, 134217727, 0, 2147483647, 0, 34359738367, 0, 549755813887, 0, 8796093022207, 0, 140737488355327, 0, 2251799813685247, 0, 36028797018963967, 0, 576460752303423487, 0, 9223372036854775807, 0

Offset

0,2

References

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

Links

Robert Price, Table of n, a(n) for n = 0..499

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 25 2015 and Apr 13 2019: (Start)

a(n) = 17*a(n-2) - 16*a(n-4) for n>5.

G.f.: (1+6*x-17*x^2+25*x^3+16*x^4-16*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).

(End)

a(n) = (2*4^n - 1)*(n mod 2) + 0^n - 0^abs(n-1). - Karl V. Keller, Jr., Aug 17 2021

Mathematica

rule=7; 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([(2*4**n-1)*(n%2) + 0**n - 0**abs(n-1) for n in range(33)]) # Karl V. Keller, Jr., Aug 17 2021

Crossrefs

Cf. A266216, A266217.

Sequence in context: A167028 A246137 A052679 * A240818 A134680 A362794

Adjacent sequences: A266215 A266216 A266217 * A266219 A266220 A266221

Keyword

nonn,easy

Author

Robert Price, Dec 24 2015

Status

approved