A350367 Triangular numbers that are the sum of two distinct nonzero triangular numbers in more than one way.

231, 276, 406, 666, 861, 1081, 1225, 1431, 1711, 1891, 2211, 2556, 3081, 3741, 3916, 4186, 4371, 4560, 4656, 5151, 5356, 5671, 5886, 6786, 7021, 7381, 7875, 8001, 8128, 8256, 8778, 9316, 10731, 11781, 12246, 12561, 12720, 13366, 13861, 14196, 14706, 15576

Offset: 1

Author

Shyam Sunder Gupta, Dec 27 2021

Keywords

• nonn

Examples

			231 = 21 + 210 = 78 + 153.
276 = 45 + 231 = 66 + 210 = 105 + 171.
		

Crossrefs

Intersection of A000217 and A262749.

Cf. A089982, A112352.

Programs

Mathematica

(P=PolygonalNumber)[3,Select[Range@176,Length@Select[Subsets[P[3,Range[s=#]],{2}],Total@#==P[3,s]&]>1&]] (* Giorgos Kalogeropoulos, Dec 31 2021 *)

Python

from collections import Counter
from itertools import count, takewhile, combinations as combs
def aupto(limit):
    tris = takewhile(lambda x: x <= limit, (k*(k+1)//2 for k in count(1)))
    trilst = list(tris); triset = set(trilst)
    tri2ct = Counter(sum(c) for c in combs(trilst, 2) if sum(c) in triset)
    return sorted(t for t in tri2ct if t <= limit and tri2ct[t] > 1)
print(aupto(16000)) # Michael S. Branicky, Dec 27 2021