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%I #12 Nov 04 2020 05:23:31
%S 3,4,5,20,21,29,119,120,169,696,697,985,4059,4060,5741,23660,23661,
%T 33461,137903,137904,195025,803760,803761,1136689,4684659,4684660,
%U 6625109,27304196,27304197,38613965,159140519,159140520,225058681
%N Pythagorean triples of nearly isosceles triangle.
%C 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.
%H C.C. Chen and T.A. Peng, <a href="https://ajc.maths.uq.edu.au/pdf/11/ocr-ajc-v11-p263.pdf">Classroom note: Almost-isosceles right-angled triangles</a>, Australasian Journal of Combinatorics, Volume 11(1995), pp. 263-267. See p. 266.
%F 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.
%e 119^2 + 120^2 = 169^2.
%o 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
%Y Cf. A001652, A001653, A046090.
%K easy,nonn,tabf
%O 1,1
%A Heinrich Baldauf (heinbald25(AT)web.de), Feb 07 2006
%E More terms from _Robert Hutchins_, Jun 10 2009
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