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Number of triangular numbers between n and 2n (inclusive).
1

%I #7 Dec 15 2017 17:36:28

%S 1,1,2,1,2,2,1,2,2,2,2,2,2,3,3,2,2,3,3,3,3,2,3,3,3,3,3,4,3,3,3,3,4,4,

%T 4,4,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,4,4,4,4,5,5,5,5,5,5,5,4,5,

%U 5,5,5,5,5,5,5,5,6,6,5,5,5,5,5,5,5,6,6,6,6,6,6,5,5,5,6,6,6,6,6,6,6,6,6,6,7

%N Number of triangular numbers between n and 2n (inclusive).

%t With[{trnos=Accumulate[Range[100]]},Table[Count[trnos,_?(n<=#<=2n&)],{n,110}]] (* _Harvey P. Dale_, Jul 23 2013 *)

%K easy,nonn

%O 1,3

%A Amarnath Murthy, _Jason Earls_, Jul 22 2003