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%I #9 Feb 10 2023 10:01:24
%S 2,1,2,3,1,2,5,3,4,1,2,7,5,8,3,4,1,2,9,7,12,5,13,8,11,3,4,1,2,11,9,16,
%T 7,19,12,17,5,18,13,21,8,14,3,4,1,2,13,11,20,9,25,16,23,7,26,19,31,12,
%U 29,17,22,5,18,34,21,8,14,3,4,1,2,15,13,24,11,31,20,29,9,34,25,41,16,39,23
%N Sum-fill array starting with (2,1).
%C The sequence represents a para-sequence.
%D Clark Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, preprint, 2007.
%H Clark Kimberling, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL25/Kimberling/kimber16.html"> Self-Containing Sequences, Selection Functions, and Parasequences</a>, J. Int. Seq. Vol. 25 (2022), Article 22.2.1.
%F Row n>=2 is produced from row n by the sum-fill operation, defined on an arbitrary infinite or finite sequence x = (x(1), x(2), x(3), ...) by the following two steps: Step 1. Form the sequence x(1), x(1)+x(2), x(2), x(2)+x(3), x(3), x(3)+x(4), ...; i.e., fill the space between x(n) and x(n+1) by their sum. Step 2. Delete duplicates; i.e., letting y be the sequence resulting from Step 1, if y(n+h)=y(n) for some h>=1, then delete y(n+h).
%e The initial row (2,1) begets (2,3,1) because 3 = 2+1.
%e Then (2,3,1) begets (2,5,3,4,1) by sum-filling, etc.
%e First 5 rows:
%e 2 1
%e 2 3 1
%e 2 5 3 4 1
%e 2 7 5 8 3 4 1
%e 1 6 5 9 4 1 7 10 3 8 2
%Y Cf. A134625, A134626, A134627.
%K nonn,tabf
%O 1,1
%A _Clark Kimberling_, Nov 04 2007