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 A350367 Triangular numbers that are the sum of two distinct nonzero triangular numbers in more than one way. 0
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified February 28 07:05 EST 2024. Contains 370387 sequences. (Running on oeis4.)