%I #7 May 19 2019 02:14:24
%S 10,28,45,55,66,91,105,120,136,153,171,190,210,231,253,276,300,325,
%T 351,378,406,435,465,496,528,561,595,630,666,703,741,780,820,861,903,
%U 946,990,1035,1081,1128,1176,1225,1275,1326,1378,1431,1485
%N Triangular numbers that are the sum of three distinct positive triangular numbers.
%C Subsequence of A112355: it doesn't require the three positive triangular numbers to be distinct.
%e 45 is a term because 45 = 3 + 6 + 36 and these four numbers are distinct triangular numbers (A000217(9) = A000217(2) + A000217(3) + A000217(8)).
%t trnos=Accumulate[Range[200]];
%t Take[Union[Select[Total/@Subsets[trnos,{3}],MemberQ[trnos,#]&]],50] (* _Harvey P. Dale_, Jan 15 2011 *)
%Y Cf. A000217 (triangular numbers), A112352 (triangular numbers that are the sum of two distinct positive triangular numbers), A112355.
%K nonn
%O 1,1
%A _Rick L. Shepherd_, Sep 05 2005
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