login
Consider the k-th row of triangle A170899 starting at the 3 in the middle of the row; the row from that point on converges to this sequence as k increases.
5

%I #19 Mar 14 2021 20:35:21

%S 3,6,11,13,13,21,33,29,17,21,37,51,51,57,77,61,25,21,37,51,55,71,111,

%T 127,91,65,93,137,143,147,175,127,41,21,37,51,55,71,111,127,95,79,119,

%U 179,207,219,271,279,171,81,93,137,159,195,291,363

%N Consider the k-th row of triangle A170899 starting at the 3 in the middle of the row; the row from that point on converges to this sequence as k increases.

%C It would be nice to have a formula or recurrence for any of A170899, A342272-A342278, or any nontrivial relation between them. This might help to understand the fractal structure of the mysterious hexagonal Ulam-Warburton cellular automaton A151723.

%C Needs a bigger b-file.

%H N. J. A. Sloane, <a href="/A342273/b342273.txt">Table of n, a(n) for n = 0..255</a>

%e Row k=6 of A170899 breaks up naturally into 7 pieces:

%e 1;

%e 2;

%e 4,4;

%e 4,8,12,8;

%e 4,8,14,18,16,20,28,16;

%e 4,8,14,18,18,26,42,42,24,20,36,50,46,50,62,32;

%e 3,6,11,13,13,21,33,29,17,21,37,51,51,57,77,61,21,15,27,34,36,52,80,80,44,38,62,81,58,73,63,0.

%e The last piece already matches the sequence for 16 terms. The number of matching terms doubles at each row.

%Y Cf. A151723, A151724, A342272.

%K nonn

%O 0,1

%A _N. J. A. Sloane_, Mar 13 2021