A185978 Nontriangular numbers which are the sum of two (positive) triangular numbers.

2, 4, 7, 9, 11, 12, 13, 16, 18, 20, 22, 24, 25, 27, 29, 30, 31, 34, 37, 38, 39, 42, 43, 46, 48, 49, 51, 56, 57, 58, 60, 61, 64, 65, 67, 69, 70, 72, 73, 76, 79, 81, 83, 84, 87, 88, 90, 92, 93, 94, 97, 99, 100, 101, 102, 106, 108

Offset: 1

Author

Wolfdieter Lang, Feb 14 2011

Keywords

• nonn
• easy

Comments

This is A051533 (sums of two positive triangular numbers) excluding triangular numbers.

This is also A020756 (sums of two triangular numbers) excluding triangular numbers.

There may be multiple representations, e.g., 16 = 1 + 15 = 6 + 10.

Examples

			a(6) = 12 = 6 + 6,
a(17) = 31 = 3 + 28 = 10 + 21.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000217, A020756 (sums of two triangular numbers), A051533 (sums of two positive triangular numbers).

Programs

Mathematica

(* First run the program for A051533 *) Complement[%, tri] (* Alonso del Arte, Feb 15 2011 *)

Formula

This is the sorted, made unique set {binomial(k+1,2) + binomial(L+1,2), 1 <= k <= L sufficiently large}, excluding members from A000217 (triangular numbers).