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, 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

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 A348163

Adjacent sequences: A319608 A319609 A319610 * A319612 A319613 A319614

Keyword

nonn

Author

Philipp O. Tsvetkov, Sep 24 2018

Status

approved