A357504 Numbers that are the sum of two distinct triangular numbers.

1, 3, 4, 6, 7, 9, 10, 11, 13, 15, 16, 18, 21, 22, 24, 25, 27, 28, 29, 31, 34, 36, 37, 38, 39, 42, 43, 45, 46, 48, 49, 51, 55, 56, 57, 58, 60, 61, 64, 65, 66, 67, 69, 70, 72, 73, 76, 78, 79, 81, 83, 84, 87, 88, 91, 92, 93, 94, 97, 99, 100, 101, 102, 105, 106, 108

Offset: 1

Author

Stefano Spezia, Oct 01 2022

Keywords

• nonn
• easy

Comments

This sequence differs from A020756 in excluding the terms that are twice a triangular number and that cannot be expressed as a sum of two distinct triangular numbers: 0, 2, 12, 20, 30, 90, 110, 132, ... = 2*A357529.

Crossrefs

Cf. A000217 (subsequence, excluding 0), A020756 (supersequence), A339952, A357505 (complement).

Cf. A357529.

Programs

Mathematica

TriangularQ[n_]:=IntegerQ[(Sqrt[1+8n]-1)/2]; A000217[n_]:=n(n+1)/2; a={}; kn=0; For[k=0, k<=110, k++, For[h=0, A000217[h]A000217[h]] && k>kn, AppendTo[a, k]; kn=k]]]; a (* Stefano Spezia, Nov 06 2022 *)

Formula

a(n) = (A339952(n) - 1)/4.