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A247586
Number of acute triangles with integer sides less than or equal to n.
4
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
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