OFFSET
1,2
LINKS
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
KEYWORD
nonn
AUTHOR
Vladimir Letsko, Sep 20 2014
STATUS
approved