A266070 Middle column of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.

1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1

Offset

0

Comments

The binomial transform is 1, 1, 1, 2, 5, 12, 27,..., i.e., A000325 with another 1 in front. The inverse binomial transform is 1, -1, 1, 0, -3, 10, -25, 56, -119, 246, -501, 1012,... essentially A000247. R. J. Mathar, Feb 16 2023

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, 1).

Formula

G.f.: (-1 + x^2 - x^3)/(-1 + x^2). - Michael De Vlieger, Dec 21 2015

Example

From Michael De Vlieger, Dec 21 2015: (Start)
First 8 rows at right, the center column values in parentheses are the values of the terms of this sequence at left:
a(1)                (1)
a(2)              1 (0) 0
a(3)            0 0 (0) 1 0
a(4)          1 1 1 (1) 0 0 1
a(5)        0 0 0 0 (0) 0 1 0 0
a(6)      1 1 1 1 1 (1) 1 0 0 1 1
a(7)    0 0 0 0 0 0 (0) 0 0 1 0 0 0
a(8)  1 1 1 1 1 1 1 (1) 1 1 0 0 1 1 1
(End)

Mathematica

Table[SeriesCoefficient[(-1 + x^2 - x^3)/(-1 + x^2), {x, 0, n}], {n, 0, 120}] (* Michael De Vlieger, Dec 21 2015 *)

Crossrefs

Cf. A263428, A266071.

Sequence in context: A004641 A266441 A266672 * A262855 A353380 A204171

Adjacent sequences: A266067 A266068 A266069 * A266071 A266072 A266073

Keyword

nonn,easy

Author

Robert Price, Dec 20 2015

Status

approved