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 A114336 Pythagorean triples of nearly isosceles triangle. 1
 3, 4, 5, 20, 21, 29, 119, 120, 169, 696, 697, 985, 4059, 4060, 5741, 23660, 23661, 33461, 137903, 137904, 195025, 803760, 803761, 1136689, 4684659, 4684660, 6625109, 27304196, 27304197, 38613965, 159140519, 159140520, 225058681 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Pythagorean triples of exact isosceles triangles do not exist because 2a^2 = c^2 has no integer solution. a^2 + (a+1)^2 = c^2 are nearly isosceles triangles and give a recursive series. LINKS C.C. Chen and T.A. Peng, Classroom note: Almost-isosceles right-angled triangles, Australasian Journal of Combinatorics, Volume 11(1995), pp. 263-267. See p. 266. FORMULA a^2 + (a+1)^2 = c^2, a(n) = 3a(n-1) + 2c(n-1) + 1, c(n) = 4a(n-1) + 3c(n-1) + 2. EXAMPLE 119^2 + 120^2 = 169^2. PROG a(1):= 3 c(1):= 5 read m C m is infinite but limited by integer overflow of c(n) for n:=2 until m step 1 a(n):= 3*a(n-1) + 2*c(n-1) + 1 c(n):= 4*a(n-1) + 3*c(n-1) + 2 print a(n), a(n)+1, c(n) next n end CROSSREFS Cf. A001652, A001653, A046090. Sequence in context: A161474 A247573 A084930 * A048086 A048005 A334638 Adjacent sequences:  A114333 A114334 A114335 * A114337 A114338 A114339 KEYWORD easy,nonn,tabf AUTHOR Heinrich Baldauf (heinbald25(AT)web.de), Feb 07 2006 EXTENSIONS More terms from Robert Hutchins, Jun 10 2009 STATUS approved

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Last modified July 26 13:40 EDT 2021. Contains 346294 sequences. (Running on oeis4.)