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approved
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proposed
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editing
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return c # Chai Wah Wu, Oct 04 2023
(Python)
from math import gcd
from sympy import integer_nthroot
def A364384(n):
if n == 1: return 1
c = 0
for v in range(0, n):
for w in range(0, n-v):
u = n-v-w
if gcd(u, v, w)==1:
v2, w2, u2 = v*v, w*(u<<2), u<<1
if v2+w2>=0:
d, r = integer_nthroot(v2+w2, 2)
if r and not ((d+v)%u2 or (d-v)%u2):
c += 1
if v>0 and w>0:
c += 1
if v2-w2>=0:
d, r = integer_nthroot(v2-w2, 2)
if r and not((d+v)%u2 or (d-v)%u2):
c += 1
if v>0 and w>0:
c += 1
return c # Chai Wah Wu, Oct 04 2023
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proposed
nqueqA364384 := proc(n) local i, u, v, w, x_1, x_2, a; a := 0; i := n; for v from 1 - i to i - 1 do for w from abs(v) - i + 1 to i - abs(v) - 1 do u := i - abs(v) - abs(w); if igcd(u, v, w) = 1 then x_1 := 1/2*(-v + sqrt(v^2 - 4*w*u))/u; x_2 := 1/2*(-v - sqrt(v^2 - 4*w*u))/u; if floor(Re(x_1)) = x_1 and floor(Re(x_2)) = x_2 then a := a + 1; end if; end if; end do; end do; end proc; seq(A364384(n), n = 1 .. 100);
local i, u, v, w, x_1, x_2, a_n, L;
L:=[];
for i from 1 to n do
a_n:=0;
for v from 1-i to i-1 do
for w from abs(v)-i+1 to i-abs(v)-1 do
u:=i-abs(v)-abs(w);
if igcd(u, v, w)=1 then
x_1:=(-v+sqrt(v**2-4*u*w))/(2*u);
x_2:=(-v-sqrt(v**2-4*u*w))/(2*u);
if floor(Re(x_1))=x_1 and floor(Re(x_2))=x_2 then
a_n:=a_n+1;
end if;
end if;
end do;
end do;
L:=[op(L), a_n]
end do;
print(L);
end proc:
approved
editing
proposed
approved
editing
proposed
local i, u, v, w, x_1, x_2, a_n, L;
L:=[];
for i from 1 to n do
a_n:=0;
for v from 1-i to i-1 do
for w from abs(v)-i+1 to i-abs(v)-1 do
u:=i-abs(v)-abs(w);
if igcd(u, v, w)=1 then
x_1:=(-v+sqrt(v**2-4*u*w))/(2*u);
x_2:=(-v-sqrt(v**2-4*u*w))/(2*u);
if floor(Re(x_1))=x_1 and floor(Re(x_2))=x_2 then
a_n:=a_n+1;
end if;
end if;
end do;
end do;
L:=[op(L), a_n]
end do;
print(L);
proposed
editing
editing
proposed