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%I #12 Mar 13 2021 10:50:42
%S 1,7,24,74,228,712,2243,7079,22370,70722,223619,707120,2236083,
%T 7071084,22360697,70710696,223606818,707106802,2236067999,7071067836,
%U 22360679800,70710678145,223606797778,707106781216,2236067977530
%N Number of twin Pythagorean triples with hypotenuse less than 10^n.
%C a(n) <= 10^(n/2)/sqrt(2). - _Robert G. Wilson v_, Jan 08 2005
%H Ravi P. Agarwal, <a href="https://doi.org/10.3390/computation8030062">Pythagorean Triples Before and after Pythagoras</a>, Computation 2020, 8(3), 62, p. 14.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TwinPythagoreanTriple.html">Twin Pythagorean Triple</a>
%e For a(2)=7 because {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {20, 21, 29}, {9, 40, 41}, {11, 60, 61}, {13, 84, 85}.
%t f[n_] := Round[ Sqrt[ (10^n - 1)/2] - 1]; a[n_] := (MatrixPower[{{1, 2, 2}, {2, 1, 2}, {2, 2, 3}}, n].{{1}, {0}, {1}})[[3, 1]]; t = Table[ a[n], {n, 2, 35}]; g[n_] := Length[ Select[t, # < 10^n &]]; Table[f[n] + g[n], {n, 25}] (* _Robert G. Wilson v_, Jan 08 2005 *)
%K nonn
%O 1,2
%A _Eric W. Weisstein_, Dec 20 2004
%E a(5) and up from _Robert G. Wilson v_, Jan 08 2005
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