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Number of triangular numbers between triangular(n) and n^2.
0

%I #5 Dec 20 2013 18:29:29

%S 0,0,0,0,1,1,1,2,2,3,3,4,4,4,5,5,6,6,6,7,7,8,8,9,9,9,10,10,11,11,11,

%T 12,12,13,13,13,14,14,15,15,16,16,16,17,17,18,18,18,19,19,20,20,21,21,

%U 21,22,22,23,23,23,24,24,25,25,26,26,26,27,27,28,28,28,29,29

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

%C Number of triangular numbers t such that n*(n+1)/2 < t < n^2.

%t nn = 110; tri = Table[n (n + 1)/2, {n, nn}]; mx = Floor[Sqrt[tri[[-1]]]]; Join[{0}, Table[Length[Intersection[tri, Range[tri[[n]] + 1, n^2 - 1]]], {n, mx}]] (* _T. D. Noe_, Dec 20 2013 *)

%Y Cf. A000217, A000290, A233473.

%Y Cf. A022846 (number of triangular numbers less than n^2).

%K nonn

%O 0,8

%A _Alex Ratushnyak_, Dec 16 2013