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

1,2

Links

Table of n, a(n) for n=1..40.

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

Example

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).

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A320272 A119639 A281376 * A107957 A000603 A003453

Adjacent sequences: A247583 A247584 A247585 * A247587 A247588 A247589

Keyword

nonn

Author

Vladimir Letsko, Sep 20 2014

Status

approved