A185979 Numbers which are the sum of two positive triangular numbers in more than one way.

16, 31, 42, 46, 51, 56, 72, 76, 81, 94, 106, 111, 121, 123, 126, 133, 141, 146, 156, 157, 172, 174, 181, 186, 191, 196, 198, 211, 216, 225, 226, 231, 237, 241, 246, 256, 259, 268, 276, 281, 286, 289, 291, 297, 301, 306, 310, 315, 321, 326, 328, 331, 336, 342, 346, 354, 361, 366, 367

Offset: 1

Author

Wolfdieter Lang, Feb 15 2011

Keywords

• nonn
• easy

Comments

This is a subsequence of A020756 (sums of two triangular numbers).

This is also a subsequence of A051533 (sums of two positive triangular numbers). This is not a subsequence of A185978 (nontriangular numbers as sums of (positive) triangular numbers). E.g., a(32)=231 is missing there because 231=A000217(21). See A185980.

For the numbers which are sums of two positive triangular numbers in exactly two ways see A064816.

The first number which can be written in exactly three ways as sums of positive triangular numbers is 81.

a(n) gives the positions where A052344 entries are >= 2: A052344(a(n)) >= 2.

Examples

			16 = 15 + 1 = 10 + 6.
81 = 45 + 36 = 66 + 15 = 78 + 3.
231= 210 + 21 = 153 + 78
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000217, A020756, A051533, A052344, A064816, A185980.