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%I #13 Nov 05 2017 19:25:29
%S 0,0,1,0,0,1,2,0,0,0,1,0,1,2,3,0,0,0,0,1,0,0,1,0,1,2,0,1,2,3,4,0,0,0,
%T 0,0,1,0,0,0,1,0,0,1,0,1,2,0,0,1,0,1,2,0,1,2,3,0,1,2,3,4,5,0,0,0,0,0,
%U 0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,1,2,0,0,0,1,0,0,1,0,1,2,0,0,1,0,1,2,0,1,2,3,0,0,1,0,1,2,0,1,2,3,0,1,2,3,4
%N Construct a triangle T(n,k) (0 <= k <= n) of strings of integers, where T(0,0) = {0}, T(n,n) = {n}, and otherwise T(n,k) is the concatenation of T(n-1,k-1) and T(n-1,k). The sequence is obtained by reading across the rows of the triangle, concatenating the successive strings.
%C The string T(n,k) contains binomial(n,k) numbers.
%e The first few rows of the triangle (where the strings T(n,k) are shown without spaces for legibility) are:
%e 0,
%e 0,1,
%e 0,01,2,
%e 0,001,012,3,
%e 0,0001,001012,0123,4,
%e 0,00001,0001001012,0010120123,01234,5,
%e ...
%Y Subtracting 1 from each term gives A265754.
%Y Cf. A007318.
%K nonn,tabf
%O 0,7
%A _N. J. A. Sloane_, Nov 05 2017