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

%I A247586 #21 Jun 19 2019 08:16:47
%S A247586 1,3,6,11,17,25,36,49,64,81,102,127,154,185,219,258,301,349,401,457,
%T A247586 520,587,660,740,824,914,1010,1114,1225,1342,1468,1600,1740,1887,2041,
%U A247586 2206,2378,2561,2750,2948
%N A247586 Number of acute triangles with integer sides less than or equal to n.
%H A247586 Vladimir Letsko, <a href="http://dxdy.ru/post909787.html#p909787">Mathematical Marathon, problem 192</a> (in Russian).
%e A247586 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).
%p A247586 tr_a:=proc(n) local a,b,c,t,d;t:=0:
%p A247586   for a to n do
%p A247586   for b from a to n do
%p A247586   for c from b to min(a+b-1,n) do
%p A247586   d:=a^2+b^2-c^2:
%p A247586   if d>0 then t:=t+1 fi
%p A247586   od od od;
%p A247586   [n,t]; end;
%t A247586 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 *)
%o A247586 (Python)
%o A247586 import itertools
%o A247586 def A247586(n):
%o A247586     I = itertools.combinations_with_replacement(range(1,n+1),3)
%o A247586     F = filter(lambda c: c[0]**2 + c[1]**2 > c[2]**2, I)
%o A247586     return len(list(F))
%o A247586 print([A247586(n) for n in range(41)]) # _Peter Luschny_, Sep 22 2014
%Y A247586 Cf. A002623, A224921, A247587, A247588, A247589.
%K A247586 nonn
%O A247586 1,2
%A A247586 _Vladimir Letsko_, Sep 20 2014