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Number of distinct integers of the form i+(i+1)+(i+2)+...+j, for 1 <= i <= j <= n.
3

%I #14 Apr 22 2014 09:56:21

%S 1,3,5,9,12,16,21,27,33,40,47,55,63,70,77,89,101,110,123,134,146,159,

%T 171,186,200,214,229,245,260,275,293,312,329,349,369,388,411,432,451,

%U 474,496,519,542,564,586,611,635,660,689,713

%N Number of distinct integers of the form i+(i+1)+(i+2)+...+j, for 1 <= i <= j <= n.

%C See also A001227 = number of ways to write n as difference of triangular numbers. - _M. F. Hasler_, Apr 20 2014

%e a(3) = 5 because the possible integers are 1,2,3=1+2,5=2+3,6=1+2+3.

%K nonn

%O 1,2

%A _Jeffrey Shallit_, Apr 19 2014