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

1,1

Links

Table of n, a(n) for n=1..42.

Example

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

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 *)

Prog

(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

Crossrefs

Intersection of A000217 and A262749.

Cf. A089982, A112352.

Sequence in context: A345795 A088289 A046009 * A337231 A117223 A160355

Adjacent sequences: A350364 A350365 A350366 * A350368 A350369 A350370

Keyword

nonn

Author

Shyam Sunder Gupta, Dec 27 2021

Status

approved