cp's OEIS Frontend

A247587 Number of obtuse triangles with integer sides at most n.

%I A247587 #23 Mar 14 2021 15:25:05
%S A247587 0,0,1,2,4,8,13,20,30,42,57,74,95,120,149,182,219,261,309,362,420,485,
%T A247587 556,632,715,806,906,1012,1125,1247,1377,1517,1666,1824,1993,2170,
%U A247587 2358,2555,2765,2986
%N A247587 Number of obtuse triangles with integer sides at most n.
%H A247587 Charles R Greathouse IV, <a href="/A247587/b247587.txt">Table of n, a(n) for n = 1..10000</a>
%H A247587 Vladimir Letsko, <a href="http://dxdy.ru/post909787.html#p909787">Mathematical Marathon, problem 192</a> (in Russian).
%e A247587 a(4) = 2 because there are 2 obtuse triangles with integer sides less than or equal to 4: (2,2,3); (2,3,4).
%p A247587 tr_o:=proc(n) local a, b, c, t, d; t:=0:
%p A247587   for a to n do
%p A247587   for b from a to n do
%p A247587   for c from b to min(a+b-1, n) do
%p A247587   d:=a^2+b^2-c^2:
%p A247587   if d<0 then t:=t+1 fi
%p A247587   od od od;
%p A247587   [n, t]; end;
%o A247587 (PARI) a(n)=sum(a=2,n-1,sum(b=a,n-1,max(0,min(n,a+b-1)-sqrtint(a^2+b^2)))) \\ _Charles R Greathouse IV_, Sep 20 2014
%o A247587 (PARI) obtuse(n)=sum(a=2,n-1, max(0, sqrtint(n^2-1-a^2)-max(a,n-a+1)+1))
%o A247587 s=0; vector(100,n, s+=obtuse(n)) \\ _Charles R Greathouse IV_, Sep 20 2014
%Y A247587 Cf. A002623, A224921, A247586, A247588, A247589.
%K A247587 nonn
%O A247587 1,4
%A A247587 _Vladimir Letsko_, Sep 20 2014