A334525 Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w^2 + 7xy = 0.

1, 5, 9, 13, 17, 21, 25, 37, 41, 45, 49, 53, 57, 61, 81, 85, 89, 93, 97, 101, 105, 125, 129, 133, 137, 141, 145, 149, 185, 189, 193, 197, 201, 205, 209, 229, 233, 237, 241, 245, 249, 253, 297, 301, 305, 309, 313, 317, 321, 333, 337, 341, 345, 349, 353, 357, 393, 397

Offset: 0

Author

Brandon Crofts, Jun 15 2020

Keywords

• nonn

Comments

If n is squarefree and not divisible by 7, a(n) = a(n-1)+4. - Robert Israel, Jul 01 2020

Links

• Brandon Crofts, Table of n, a(n) for n = 0..20000
• Brandon Crofts, Mathematica code for A334525

Crossrefs

Cf. A211423.

Programs

Maple

df:= proc(n) local t, s, m0, m;
   if n mod 7 = 0 then
     m:= n/7;
     t:= 4*nops(select(s -> s < n and s > m, numtheory:-divisors(7*m^2)))
   else t:= 0
   fi;
   m0:= mul(`if`(s[1]=7, s[1]^ceil((s[2]-1)/2),
       s[1]^ceil(s[2]/2)), s=ifactors(n)[2]);
   t + 4 + 8*floor(n/m0/7);
end proc:
df(0):= 1:
ListTools:-PartialSums(map(df, [$0..100])); # Robert Israel, Jul 01 2020