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A319611 a(n) is the number of gaps in the n-th generation of the rule-30 1D cellular automaton started from a single ON. 0
0, 0, 1, 1, 2, 2, 3, 2, 3, 4, 5, 5, 6, 6, 7, 6, 6, 7, 9, 8, 8, 10, 13, 11, 10, 11, 14, 15, 13, 14, 16, 13, 14, 16, 19, 17, 17, 17, 20, 20, 16, 18, 20, 19, 22, 21, 22, 21, 22, 20, 26, 29, 25, 26, 28, 28, 27, 27, 32, 30, 29, 30, 35, 31, 27, 28, 32, 32, 32, 34, 37, 30, 27, 36, 37, 39, 42, 41, 43, 41, 34 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

OFF cells outside the triangle of active cells are ignored.

LINKS

Table of n, a(n) for n=0..80.

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)= (1)

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

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

6                . . 0 . . . . 0 . . .                   a(6)= (2)

7              . . 0 0 . 0 0 0 0 . 0 0 .                 a(7)= (3)

8            . . 0 . . . . 0 0 . . . . . .               a(8)= (2)

9          . . 0 0 . 0 0 0 . . . 0 0 0 0 0 .             a(9)= (3)

10       . . 0 . . . . 0 . . 0 0 . 0 0 0 . . .           a(10)=(4)

11     . . 0 0 . 0 0 0 0 . 0 . . . . 0 . . 0 0 .         a(11)=(5)

12   . . 0 . . . . 0 0 . . 0 . 0 0 0 0 . 0 . . . .       a(12)=(5)

13 . . 0 0 . 0 0 0 . . . 0 0 . . 0 0 . . 0 . 0 0 0 .     a(13)=(6)

MATHEMATICA

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

(Reverse[Internal`DeleteTrailingZeros[

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

Table[

Length /@ Select[%[[i]] // Split, Total[#] == 0 &] // Length,

{i, 1, % // Length}

]

CROSSREFS

Cf. A100053.

Sequence in context: A048621 A308048 A335967 * A337102 A239495 A298210

Adjacent sequences:  A319608 A319609 A319610 * A319612 A319613 A319614

KEYWORD

nonn

AUTHOR

Philipp O. Tsvetkov, Sep 24 2018

STATUS

approved

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Last modified August 3 22:03 EDT 2021. Contains 346441 sequences. (Running on oeis4.)