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A319610 a(n) is the minimal number of successive OFF cells that appears in n-th generation of rule-30 1D cellular automaton started from a single ON cell. 2
0, 0, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

OFF cells outside the triangle of active cells are ignored.

LINKS

Table of n, a(n) for n=0..138.

Charlie Neder, Repeating pattern of length-1 runs

FORMULA

G.f.: x (x + x/(1 - x) + x^3 + x^5 + x^7) (conjectured).

For n > 9, a(n)=1 at least up to n = 20000.

It is conjectured that for all n>=10, a(n)=1.

A period-4 pattern of length-1 runs starting at row 26 forces a(n) = 1 for all n >= 26 (see image). - Charlie Neder, Dec 15 2018

EXAMPLE

The Rule-30 1D cellular automaton started from a single ON (.) cell generates the following triangle:

1                          .                             a(1)= (0)

2                        . . .                           a(2)= (0)

3                      . . 0 0 .                         a(3)= (2)

4                    . . 0 . . . .                       a(4)= (1)

5                  . . 0 0 . 0 0 0 .                     a(5)= (2)

6                . . 0 . . . . 0 . . .                   a(6)= (1)

7              . . 0 0 . 0 0 0 0 . 0 0 .                 a(7)= (2)

8            . . 0 . . . . 0 0 . . . . . .               a(8)= (1)

9          . . 0 0 . 0 0 0 . . . 0 0 0 0 0 .             a(9)= (2)

10       . . 0 . . . . 0 . . 0 0 . 0 0 0 . . .           a(10)=(1)

11     . . 0 0 . 0 0 0 0 . 0 . . . . 0 . . 0 0 .         a(11)=(1)

12   . . 0 . . . . 0 0 . . 0 . 0 0 0 0 . 0 . . . .       a(12)=(1)

13 . . 0 0 . 0 0 0 . . . 0 0 . . 0 0 . . 0 . 0 0 0 .     a(13)=(1)

MATHEMATICA

CellularAutomaton[30, {{1}, 0}, 200];

(Reverse[Internal`DeleteTrailingZeros[Reverse[Internal`DeleteTrailingZeros[#]]]]) & /@ %;

Table[Length /@ Select[%[[i]] // Split, Total[#] == 0 &] // Min, {i, 1, % // Length}]

CROSSREFS

Cf. A100053.

Sequence in context: A280535 A221171 A333688 * A288739 A111621 A326398

Adjacent sequences:  A319607 A319608 A319609 * A319611 A319612 A319613

KEYWORD

nonn

AUTHOR

Philipp O. Tsvetkov, Sep 24 2018

STATUS

approved

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Last modified August 1 14:14 EDT 2021. Contains 346391 sequences. (Running on oeis4.)