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%I
%S 1,2,1,3,3,1,4,2,4,1,5,4,4,5,1,6,3,2,3,6,1,7,5,5,5,5,7,1,8,4,5,2,5,4,
%T 8,1,9,6,3,6,6,3,6,9,1,10,5,6,4,2,4,6,5,10,1,11,7,6,6,7,7,6,6,7,11,1,
%U 12,6,4,3,6,2,6,3,4,6,12,1,13,8,7,7,6,8,8,6,7
%N Triangular array T given by rows: T(n,k)=sum of quotients when Euclidean algorithm acts on n and k; for k=1,2,...,n; n=1,2,3,...
%C First quotient=[ n/k ]=Q1; 2nd=[ k/(n-k*Q1) ]; ...
%C Number of squares in a greedy tiling of an n-by-k rectangle by squares. [David Radcliffe, Nov 14 2012]
%e Rows:
%e 1;
%e 2,1;
%e 3,3,1;
%e 4,2,4,1;
%e 5,4,4,5,1;
%e 6,3,2,3,6,1;
%e 7,5,5,5,5,7,1;
%e ...
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_
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