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A177443 Triangle, row sums = A007729; derived from the generator for A002487, Stern's diatomic series.

%I A177443 #10 Dec 14 2023 08:56:56
%S A177443 1,2,0,3,1,0,3,2,0,0,3,3,2,0,0,3,3,4,0,0,0,3,3,6,1,0,0,0,3,3,6,2,0,0,
%T A177443 0,0,3,3,6,3,3,0,0,0,0,3,3,6,3,6,0,0,0,0,0,3,3,6,3,9,2,0,0,0,0,0,3,3,
%U A177443 6,3,9,4,0,0,0,0,0,0,3,3,6,3,9,6,3
%N A177443 Triangle, row sums = A007729; derived from the generator for A002487, Stern's diatomic series.
%C A177443 Rows apparently tend to 3 * nonzero terms of Stern's diatomic series; i.e.,
%C A177443 3 * (1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5,...) = (3, 3, 6, 3, 9, 6, 9, 3, 12,...)
%C A177443 Row sums = A007729: (1, 2, 4, 5, 8, 10, 13, 14, ...)
%F A177443 Triangle read by rows, Q*R*S; where Q = an infinite lower triangular matrix with all 1's, R = the generator for A002487, and S = a diagonalized variant of A002487 (nonzero terms of A002487 as the right diagonal and the rest zeros). R, the generator for A002487 is an irregular lower triangular matrix with (1, 1, 1, 0, 0, 0,...) in each column; but each successive column for k>0 is shifted down twice from the previous column.
%e A177443 First few rows of the triangle =
%e A177443 1;
%e A177443 2, 0;
%e A177443 3, 1, 0;
%e A177443 3, 2, 0, 0;
%e A177443 3, 3, 2, 0, 0;
%e A177443 3, 3, 4, 0, 0, 0;
%e A177443 3, 3, 6, 1, 0, 0, 0;
%e A177443 3, 3, 6, 2, 0, 0, 0, 0;
%e A177443 3, 3, 6, 3, 3, 0, 0, 0, 0;
%e A177443 3, 3, 6, 3, 6, 0, 0, 0, 0, 0;
%e A177443 3, 3, 6, 3, 9, 2, 0, 0, 0, 0, 0;
%e A177443 3, 3, 6, 3, 9, 4, 0, 0, 0, 0, 0, 0;
%e A177443 3, 3, 6, 3, 9, 6, 3, 0, 0, 0, 0, 0, 0;
%e A177443 3, 3, 6, 3, 9, 6, 6, 0, 0, 0, 0, 0, 0, 0;
%e A177443 3, 3, 6, 3, 9, 6, 9, 1, 0, 0, 0, 0, 0, 0, 0;
%e A177443 3, 3, 6, 3, 9, 6, 9, 2, 0, 0, 0, 0, 0, 0, 0, 0;
%e A177443 3, 3, 6, 3, 9, 6, 9, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0;
%e A177443 3, 3, 6, 3, 9, 6, 9, 3, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A177443 3, 3, 6, 3, 9, 6, 9, 3, 12, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A177443 ...
%Y A177443 Cf. A002487, A007729.
%K A177443 nonn,tabl,uned
%O A177443 0,2
%A A177443 _Gary W. Adamson_, May 08 2010