%I #29 Jul 14 2024 17:38:19

%S 1,50,878,12467,161431,1980636,23471468,271360645,3080075423,

%T 34465432849,381301109908,4179478903380,45459467009955,

%U 491241450001314,5278882299478781,56453500988940599,601181789833245614,6378285697775544212

%N Number of Pythagorean triples with hypotenuse < 10^n.

%C There seems to be a relation between A101930 and this sequence: A101930(n) = n + a(n). - Jan Feitsma and Bart Dopheide (dopheide(AT)fmf.nl), Mar 10 2005

%C A101930(n) - a(n) = A046080(10^n). The formula listed for A046080 supports the relation of Jan Feitsma and Bart Dopheide: A046080(10^n) = n. - Frank Marcoline (fvmarcoline(AT)gmail.com), Dec 10 2008

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple</a>

%F a(n) = A101930(n) - n. - _Robert G. Wilson v_, Mar 20 2014

%o (PARI) a(n)=my(t, lim=10^n-1); for(m=2, sqrtint(lim-1), forstep(n=1+m%2, min(sqrtint(lim-m^2), m-1), 2, if(gcd(m, n)==1, t+=lim\(m^2+n^2)))); t \\ _Charles R Greathouse IV_, Sep 15 2012

%Y Cf. A101930.

%K nonn

%O 1,2

%A _Eric W. Weisstein_, Dec 21 2004

%E More terms from Jan Feitsma and Bart Dopheide (dopheide(AT)fmf.nl), Mar 10 2005

%E a(10)-a(11) from _Charles R Greathouse IV_, Sep 15 2012

%E a(12)-a(17) from _Hiroaki Yamanouchi_, Jul 14 2014

%E a(18) from _Matan M. Atzmoni_, Feb 04 2023