A247586 Number of acute triangles with integer sides less than or equal to n.

1, 3, 6, 11, 17, 25, 36, 49, 64, 81, 102, 127, 154, 185, 219, 258, 301, 349, 401, 457, 520, 587, 660, 740, 824, 914, 1010, 1114, 1225, 1342, 1468, 1600, 1740, 1887, 2041, 2206, 2378, 2561, 2750, 2948

Offset: 1

Author

Vladimir Letsko, Sep 20 2014

Keywords

• nonn

Examples

			a(2) = 3 because there are 3 acute triangles with integer sides less than or equal to 2: (1,1,1); (1,2,2); (2,2,2).
		

Links

• Vladimir Letsko, Mathematical Marathon, problem 192 (in Russian).

Crossrefs

Cf. A002623, A224921, A247587, A247588, A247589.

Programs

Maple

tr_a:=proc(n) local a,b,c,t,d;t:=0:
  for a to n do
  for b from a to n do
  for c from b to min(a+b-1,n) do
  d:=a^2+b^2-c^2:
  if d>0 then t:=t+1 fi
  od od od;
  [n,t]; end;

Mathematica

a[n_] := Module[{a, b, c, d, t = 0}, Do[d = a^2 + b^2 - c^2; If[d>0, t++], {a, n}, {b, a, n}, {c, b, Min[a+b-1, n]}]; t]; Array[a, 40] (* Jean-François Alcover, Jun 19 2019, from Maple *)

Python

import itertools
def A247586(n):
    I = itertools.combinations_with_replacement(range(1,n+1),3)
    F = filter(lambda c: c[0]**2 + c[1]**2 > c[2]**2, I)
    return len(list(F))
print([A247586(n) for n in range(41)]) # Peter Luschny, Sep 22 2014