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A342274 Consider the k-th row of triangle A170899, which has 2^k terms; discard the first quarter of the terms in the row; the remainder of the row converges to this sequence as k increases.

%I A342274 #23 Mar 14 2021 20:35:41
%S A342274 4,8,14,18,18,26,42,42,26,26,46,66,70,74,98,90,42,26,46,66,74,90,138,
%T A342274 170,134,90,114,174,194,194,226,190,74,26,46,66,74,90,138,170,138,106,
%U A342274 146,226,274,290,346,378,262,122,114,174,210,250,362,474
%N A342274 Consider the k-th row of triangle A170899, which has 2^k terms; discard the first quarter of the terms in the row; the remainder of the row converges to this sequence as k increases.
%C A342274 This could be divided by 2 but then it would no longer be compatible with A342272 and A342273.
%C A342274 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.
%e A342274 Row k=6 of A170899 breaks up naturally into 7 pieces:
%e A342274 1;
%e A342274 2;
%e A342274 4,4;
%e A342274 4,8,12,8;
%e A342274 4,8,14,18,16,20,28,16;
%e A342274 4,8,14,18,18,26,42,42,24,20,36,50,46,50,62,32;
%e A342274 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 A342274 The penultimate piece matches the sequence for 8 terms. The number of matching terms doubles at each row.
%Y A342274 Cf. A151723, A170899,
%K A342274 nonn
%O A342274 0,1
%A A342274 _N. J. A. Sloane_, Mar 13 2021