|
%I #59 Feb 26 2018 09:16:40
%S 0,17,325,4858,64741,808950,9706567,113236940,1294080089,14557915466
%N Number of Pythagorean triples with perimeter <= 10^n.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tree_of_primitive_Pythagorean_triples">Tree of primitive Pythagorean triples</a>
%e n = 2
%e perimeter | Pythagorean triple
%e -------------------------------
%e 12 | [ 3, 4, 5]
%e 30 | [ 5, 12, 13]
%e 24 | [ 6, 8, 10]
%e 56 | [ 7, 24, 25]
%e 40 | [ 8, 15, 17]
%e 36 | [ 9, 12, 15]
%e 90 | [ 9, 40, 41]
%e 60 | [10, 24, 26]
%e 48 | [12, 16, 20]
%e 84 | [12, 35, 37]
%e 60 | [15, 20, 25]
%e 90 | [15, 36, 39]
%e 80 | [16, 30, 34]
%e 72 | [18, 24, 30]
%e 70 | [20, 21, 29]
%e 84 | [21, 28, 35]
%e 96 | [24, 32, 40]
%o (Ruby)
%o def f(a, b, c, n)
%o return 0 if a + b + c > n
%o s = n / (a + b + c)
%o s += f( a - 2 * b + 2 * c, 2 * a - b + 2 * c, 2 * a - 2 * b + 3 * c, n)
%o s += f( a + 2 * b + 2 * c, 2 * a + b + 2 * c, 2 * a + 2 * b + 3 * c, n)
%o s += f(-a + 2 * b + 2 * c, -2 * a + b + 2 * c, -2 * a + 2 * b + 3 * c, n)
%o return s
%o end
%o def A299706(n)
%o (1..n).map{|i| f(3, 4, 5, 10 ** i)}
%o end
%o p A299706(8)
%Y Cf. A024155, A101929, A101930, A101931, A249750.
%K nonn,more
%O 1,2
%A _Seiichi Manyama_, Feb 26 2018
|
