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A299706 Number of Pythagorean triples with perimeter <= 10^n.

%I A299706 #60 Feb 16 2025 08:33:53
%S A299706 0,17,325,4858,64741,808950,9706567,113236940,1294080089,14557915466
%N A299706 Number of Pythagorean triples with perimeter <= 10^n.
%H A299706 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple</a>
%H A299706 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tree_of_primitive_Pythagorean_triples">Tree of primitive Pythagorean triples</a>
%e A299706 n = 2
%e A299706 perimeter | Pythagorean triple
%e A299706 -------------------------------
%e A299706    12     | [ 3,  4,  5]
%e A299706    30     | [ 5, 12, 13]
%e A299706    24     | [ 6,  8, 10]
%e A299706    56     | [ 7, 24, 25]
%e A299706    40     | [ 8, 15, 17]
%e A299706    36     | [ 9, 12, 15]
%e A299706    90     | [ 9, 40, 41]
%e A299706    60     | [10, 24, 26]
%e A299706    48     | [12, 16, 20]
%e A299706    84     | [12, 35, 37]
%e A299706    60     | [15, 20, 25]
%e A299706    90     | [15, 36, 39]
%e A299706    80     | [16, 30, 34]
%e A299706    72     | [18, 24, 30]
%e A299706    70     | [20, 21, 29]
%e A299706    84     | [21, 28, 35]
%e A299706    96     | [24, 32, 40]
%o A299706 (Ruby)
%o A299706 def f(a, b, c, n)
%o A299706   return 0 if a + b + c > n
%o A299706   s = n / (a + b + c)
%o A299706   s += f( a - 2 * b + 2 * c,  2 * a - b + 2 * c,  2 * a - 2 * b + 3 * c, n)
%o A299706   s += f( a + 2 * b + 2 * c,  2 * a + b + 2 * c,  2 * a + 2 * b + 3 * c, n)
%o A299706   s += f(-a + 2 * b + 2 * c, -2 * a + b + 2 * c, -2 * a + 2 * b + 3 * c, n)
%o A299706   return s
%o A299706 end
%o A299706 def A299706(n)
%o A299706   (1..n).map{|i| f(3, 4, 5, 10 ** i)}
%o A299706 end
%o A299706 p A299706(8)
%Y A299706 Cf. A024155, A101929, A101930, A101931, A249750.
%K A299706 nonn,more
%O A299706 1,2
%A A299706 _Seiichi Manyama_, Feb 26 2018