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

1,5

Links

Table of n, a(n) for n=1..50.

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

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

Example

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

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;

Crossrefs

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

Sequence in context: A092311 A335365 A186386 * A361070 A058212 A007997

Adjacent sequences: A247586 A247587 A247588 * A247590 A247591 A247592

Keyword

nonn

Author

Vladimir Letsko, Sep 20 2014

Status

approved