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A350368 Triangular numbers that are the sum of two distinct nonzero triangular numbers in exactly two ways. 0
231, 1081, 1225, 1431, 1711, 2556, 5356, 7381, 7875, 8256, 15931, 19306, 20706, 26106, 30381, 33153, 36856, 46056, 51681, 75078, 78606, 102831, 104653, 135981, 149331, 153181, 182106, 197506, 225456, 263175, 265356, 316410, 317206, 336610, 379756, 424581 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..36.

EXAMPLE

231 = 21 + 210 = 78 + 153.

1081 = 91 + 990 = 378 + 703.

MATHEMATICA

(P=PolygonalNumber)[3, Select[Range@200, Length@Select[Subsets[P[3, Range[s=#]], {2}], Total@#==P[3, s]&]==2&]] (* 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] == 2)

print(aupto(500000)) # Michael S. Branicky, Dec 27 2021

CROSSREFS

Intersection of A000217 and A265134.

Sequence in context: A246886 A258167 A287472 * A183672 A183664 A260302

Adjacent sequences:  A350365 A350366 A350367 * A350369 A350370 A350371

KEYWORD

nonn

AUTHOR

Shyam Sunder Gupta, Dec 27 2021

STATUS

approved

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Last modified August 14 13:43 EDT 2022. Contains 356117 sequences. (Running on oeis4.)