A110266 Number of blocks of ON cells in n-th row of triangle generated by Wolfram's "Rule 30".

1, 1, 2, 2, 3, 3, 4, 3, 4, 5, 6, 6, 7, 7, 8, 7, 7, 8, 10, 9, 9, 11, 14, 12, 11, 12, 15, 16, 14, 15, 17, 14, 15, 17, 20, 18, 18, 18, 21, 21, 17, 19, 21, 20, 23, 22, 23, 22, 23, 21, 27, 30, 26, 27, 29, 29, 28, 28, 33, 31, 30, 31, 36, 32, 28, 29, 33, 33, 33, 35

Offset: 1

Author

Alexandre Wajnberg, Sep 06 2005

Keywords

• easy
• nonn

Comments

Old name was "Number of trees appearing at n-th generation of a black cell following Wolfram's Rule 30 cellular automaton."

At each generation, "looking back", one can see "behind", groups (sort of black isles) of contiguous black cells which after a while appear to be trees growing. It should be possible to describe each one of them in terms of trees theory.

Examples

			a(1)=1 because one black cell;
a(2)=1 because there are now 3 contiguous black cell connected to the first one, which forms one only black surface;
a(3)=2 because two black cells are now connected to the preceding black surface and another black cell appears, which is isolated, so we have two separate black surfaces: 2.
From _Charlie Neder_, Feb 06 2019: (Start)
Rule 30 triangle begins:
                     1
                    111
                   11  1
                  11 1111
                 11  1   1
                11 1111 111
               11  1    1  1
              11 1111  111111
             11  1   111     1
and the number of blocks of ON cells in each row is 1, 1, 2, 2, 3, 3, 4, 3, 4, ... (End)
		

Links

• Charlie Neder, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Rule 30.

Crossrefs

Cf. A070950, A051023, A092539, A092540, A070952, A100053, A100054, A100055, A094603, A094604, A000225, A074890.

Extensions

New name and a(17)-a(70) from Charlie Neder, Feb 06 2019