A350367 - OEIS

%I #18 Feb 06 2022 21:29:19

%S 231,276,406,666,861,1081,1225,1431,1711,1891,2211,2556,3081,3741,

%T 3916,4186,4371,4560,4656,5151,5356,5671,5886,6786,7021,7381,7875,

%U 8001,8128,8256,8778,9316,10731,11781,12246,12561,12720,13366,13861,14196,14706,15576

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

%e 231 = 21 + 210 = 78 + 153.

%e 276 = 45 + 231 = 66 + 210 = 105 + 171.

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

%o (Python)

%o from collections import Counter

%o from itertools import count, takewhile, combinations as combs

%o def aupto(limit):

%o     tris = takewhile(lambda x: x <= limit, (k*(k+1)//2 for k in count(1)))

%o     trilst = list(tris); triset = set(trilst)

%o     tri2ct = Counter(sum(c) for c in combs(trilst, 2) if sum(c) in triset)

%o     return sorted(t for t in tri2ct if t <= limit and tri2ct[t] > 1)

%o print(aupto(16000)) # _Michael S. Branicky_, Dec 27 2021

%Y Intersection of A000217 and A262749.

%Y Cf. A089982, A112352.

%K nonn

%O 1,1

%A _Shyam Sunder Gupta_, Dec 27 2021