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A122513
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Numbers n such that 1+2n+3n^2 is a triangular number.
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0
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0, 1, 46, 135, 4540, 13261, 444906, 1299475, 43596280, 127335321, 4271990566, 12477562015, 418611479220, 1222673742181, 41019652973026, 119809549171755, 4019507379877360, 11740113145089841, 393870703575008286, 1150411278669632695, 38595309442970934700
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The y solution to the generalized Pell equation x^2 + x = 2 + 4*y + 6*y^2. - T. D. Noe, Apr 28 2011
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EXAMPLE
| Corresponding values of triangular numbers tri=m(m+1)/2 and m's are
tri = 1, 6, 6441, 54946, 61843881, 527588886, 593824936321
m = 1, 3, 113, 331, 11121, 32483, 1089793
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MATHEMATICA
| triQ[n_] := IntegerQ[ Sqrt[8n + 1]]; lst = {}; Do[ If[ triQ[1 + 2n + 3n^2], AppendTo[lst, n]; Print@n], {n, 0, 65000000}] (* Robert G. Wilson v *)
LinearRecurrence[{1, 98, -98, -1, 1}, {1, 46, 135, 4540, 13261}, 30] (* T. D. Noe, Apr 28 2011 *)
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CROSSREFS
| Cf. A000217 = triangular numbers, A086285 = numbers n such that 1+2n+3n^2 is prime.
Sequence in context: A044297 A044678 A074866 * A053019 A044378 A044759
Adjacent sequences: A122510 A122511 A122512 * A122514 A122515 A122516
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KEYWORD
| nonn
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Oct 20 2006
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EXTENSIONS
| a(8) & a(9) from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 08 2007
a(10)-a(11) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Apr 28 2011
Extended by T. D. Noe (noe(AT)sspectra.com), Apr 28 2011
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