Original entry on oeis.org
1, 3, 7, 13, 25, 41, 65, 93, 133, 177, 245, 305, 397, 489, 609, 725, 893, 1029, 1241, 1425, 1665, 1889, 2209, 2457, 2821, 3145, 3549, 3913, 4429, 4805, 5397, 5885, 6493, 7045, 7781, 8341, 9185, 9881, 10745, 11489, 12545, 13297, 14453, 15385, 16497, 17517, 18917
Offset: 1
-
A381711:=proc(n)
option remember;
local a,u,v,w;
if n=1 then
1
else
a:=0;
for u to n-1 do
for v from 0 to n-u do
w:=n-u-v;
if igcd(u,v,w)=1 and v<>0 then
if w=0 or w=v^2/(4*u) then
a:=a+2
elif wA381711(n),n=1..47);
A379597
a(n) is the number of distinct solution sets to the quadratic equations u*x^2 + v*x + w = 0 with integer coefficients u, v, w, abs(u) + abs(v) + abs(w) <= n having a nonnegative discriminant.
Original entry on oeis.org
1, 4, 12, 24, 50, 80, 134, 192, 276, 366, 510, 632, 834, 1018, 1262, 1502, 1858, 2136, 2584, 2956, 3448, 3910, 4576, 5076, 5834, 6488, 7320, 8066, 9136, 9892, 11118, 12114, 13358, 14482, 15978, 17108, 18862, 20272, 22024, 23532, 25700, 27216, 29600, 31486, 33746
Offset: 1
a(3) = 12 because there are 12 equations with abs(u) + abs(v) + abs(w) <= 3 and distinct solution set having a nonnegative discriminant: (u, v, w) = (1, 0, 0), (1, -1, 0), (1, 1, 0), (1, 0, -1), (1, -1, -1), (1, 1, -1), (1, -2, 0), (1, 2, 0), (1, 0, -2), (2, -1, 0), (2, 1, 0), and (2, 0, -1). Multiplied equations like 2*(1, 0, 0) = (2, 0, 0) or (-1)*(1, -1, 0) = (-1, 1, 0) do not have a distinct solution set.
-
A379597:=proc(n)
option remember;
local a,u,v,w;
if n=1 then
1
else
a:=0;
for u to n-1 do
for v from 0 to n-u do
w:=n-u-v;
if igcd(u,v,w)=1 then
if v=0 then
a:=a+1
elif w=0 or w>=v^2/(4*u) then
a:=a+2
else
a:=a+4
fi
fi
od
od;
a+procname(n-1)
fi;
end proc;
seq(A379597(n),n=1..45);
Showing 1-2 of 2 results.
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