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

1,1

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.

Links

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

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).

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A047541 A308496 A226812 * A351799 A120749 A187978

Adjacent sequences: A185975 A185976 A185977 * A185979 A185980 A185981

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 14 2011

Status

approved