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

Author

Philipp O. Tsvetkov, Sep 24 2018

Keywords

• nonn

Comments

OFF cells outside the triangle of active cells are ignored.

Examples

			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)
		

Crossrefs

Cf. A100053.

Programs

Mathematica

CellularAutomaton[30, {{1}, 0}, 200];
(Reverse[Internal`DeleteTrailingZeros[
      Reverse[Internal`DeleteTrailingZeros[#]]]]) & /@ %;
Table[
Length /@ Select[%[[i]] // Split, Total[#] == 0 &] // Length,
{i, 1, % // Length}
]