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A247589 Number of integer-sided obtuse triangles with largest side n.

%I A247589 #21 Sep 05 2021 18:23:25
%S A247589 0,0,1,1,2,4,5,7,10,12,15,17,21,25,29,33,37,42,48,53,58,65,71,76,83,
%T A247589 91,100,106,113,122,130,140,149,158,169,177,188,197,210,221,230,243,
%U A247589 255,269,281,292,306,318,333,346
%N A247589 Number of integer-sided obtuse triangles with largest side n.
%H A247589 Vladimir Letsko, <a href="http://dxdy.ru/post909787.html#p909787">Mathematical Marathon, problem 192</a> (in Russian).
%F A247589 a(n) = k*(k + (1+(-1)^n)/2) + Sum_{j=1..floor(n*(1-sqrt(2)/2))} floor(sqrt(2*j*n - j^2 - 1) - j), where k = floor((2*n*(sqrt(2) - 1) + 1 - (-1)^n)/4) (it appears that k(n) is A070098(n)). - _Anton Nikonov_, Sep 29 2014
%e A247589 a(5) = 2 because there are 2 integer-sided acute triangles with largest side 5: (2,4,5); (3,3,5).
%p A247589 tr_o:=proc(n) local a,b,t,d;t:=0:
%p A247589 for a to n do
%p A247589 for b from max(a,n+1-a) to n do
%p A247589 d:=a^2+b^2-n^2:
%p A247589 if d<0 then t:=t+1 fi
%p A247589 od od;
%p A247589 t; end;
%Y A247589 Cf. A046080, A002623, A224921, A247586, A247587, A247588.
%K A247589 nonn
%O A247589 1,5
%A A247589 _Vladimir Letsko_, Sep 20 2014