A225206 - OEIS

%I #23 Mar 01 2023 01:49:37

%S 6,571,56268,5614390,561232920,56120665334,5612026652893,

%T 561202243017532,56120219419339591

%N Number of Pythagorean quadruples (a, b, c, d) with d < 10^n.

%C a(n) ~ Pi*A225207(n)/(1+G), where G is Catalan's constant (A006752).

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Pythagorean_quadruple">Pythagorean quadruple</a>

%F a(n) = Sum_{k=1..10^n-1} A181786(k). - _Max Alekseyev_, Feb 28 2023

%e a(1) = 6 because there are six solutions (a, b, c, d) as follows: (1, 2, 2, 3), (2, 4, 4, 6), (2, 3, 6, 7), (1, 4, 8, 9), (3, 6, 6, 9), (4, 4, 7, 9) with d < 10.

%Y Cf. A169580, A181786, A225207.

%K more,nonn

%O 1,1

%A _Arkadiusz Wesolowski_, May 01 2013

%E a(4) from _Giovanni Resta_, May 01 2013

%E a(5)-a(9) from _Max Alekseyev_, Feb 28 2023