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

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, 91, 100, 106, 113, 122, 130, 140, 149, 158, 169, 177, 188, 197, 210, 221, 230, 243, 255, 269, 281, 292, 306, 318, 333, 346

Offset: 1

Author

Vladimir Letsko, Sep 20 2014

Keywords

• nonn

Examples

			a(5) = 2 because there are 2 integer-sided acute triangles with largest side 5: (2,4,5); (3,3,5).
		

Links

• Vladimir Letsko, Mathematical Marathon, problem 192 (in Russian).

Crossrefs

Cf. A046080, A002623, A224921, A247586, A247587, A247588.

Programs

Maple

tr_o:=proc(n) local a,b,t,d;t:=0:
for a to n do
for b from max(a,n+1-a) to n do
d:=a^2+b^2-n^2:
if d<0 then t:=t+1 fi
od od;
t; end;

Formula

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