A224921 Number of Pythagorean triples (a, b, c) with a^2 + b^2 = c^2 and 0 < a < b < c < n.

0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 8, 9, 9, 9, 10, 11, 11, 11, 11, 12, 13, 13, 14, 14, 15, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 20, 21, 22, 23, 23, 24, 24, 24, 25, 25, 26, 27, 27, 27, 27, 31, 31, 31, 32, 32, 33, 33, 33

Offset: 1

Author

Reiner Moewald, Apr 19 2013

Keywords

• nonn

Comments

a(n+1) > a(n) iff n is in A009003. - Benoit Cloitre, Dec 08 2021

Links

• Reiner Moewald and Robert Israel, Table of n, a(n) for n = 1..10000 (n = 1..500 from Reiner Moewald)

Crossrefs

Cf. A156685. Essentially partial sums of A046080.

Cf. A009003.

Programs

Maple

a046080:= proc(n) local F,t;
  F:= select(t -> t[1] mod 4 = 1, ifactors(n)[2]);
  1/2*(mul(2*t[2]+1, t=F)-1)
end proc:
ListTools:-PartialSums(map(a046080, [$0..100])); # Robert Israel, Jul 18 2016

Mathematica

b[0] = b[1] = 0; b[n_] := With[{fi = Select[FactorInteger[n], Mod[#[[1]], 4] == 1&][[All, 2]]}, (Times @@ (2*fi + 1) - 1)/2];
Table[b[n], {n, 0, 100}] // Accumulate (* Jean-François Alcover, Feb 27 2019 *)

PARI

a(n)=sum(a=1,n-3,sum(b=a+1,sqrtint((n-1)^2-a^2), issquare(a^2+b^2))) \\ Charles R Greathouse IV, Apr 29 2013