A112353 Triangular numbers that are the sum of three distinct positive triangular numbers.

10, 28, 45, 55, 66, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431, 1485

Offset: 1

Author

Rick L. Shepherd, Sep 05 2005

Keywords

• nonn

Comments

Subsequence of A112355: it doesn't require the three positive triangular numbers to be distinct.

Examples

			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)).
		

Crossrefs

Cf. A000217 (triangular numbers), A112352 (triangular numbers that are the sum of two distinct positive triangular numbers), A112355.

Programs

Mathematica

trnos=Accumulate[Range[200]];
Take[Union[Select[Total/@Subsets[trnos,{3}],MemberQ[trnos,#]&]],50]  (* Harvey P. Dale, Jan 15 2011 *)