A334524 Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w^2 + 5xy = 0.

1, 5, 9, 13, 17, 29, 33, 37, 41, 45, 65, 69, 73, 77, 81, 101, 105, 109, 113, 117, 153, 157, 161, 165, 169, 181, 185, 189, 193, 197, 233, 237, 241, 245, 249, 261, 273, 277, 281, 285, 321, 325, 329, 333, 337, 373, 377, 381, 385, 397, 417, 421, 425, 429, 433, 445

Offset: 0

Author

Brandon Crofts, Jun 15 2020

Keywords

• nonn

Comments

If n is squarefree and not divisible by 5, a(n) = a(n-1)+4. - Robert Israel, Jun 29 2020

Links

• Brandon Crofts, Table of n, a(n) for n = 0..20000 (first 10001 terms from Robert Israel)
• Brandon Crofts, Mathematica code for 334524

Crossrefs

Cf. A211423.

Programs

Maple

df:= proc(n) local t,s,m0,m;
   if n mod 5 = 0 then
     m:= n/5;
     t:= 4*nops(select(s -> s < n and s > m, numtheory:-divisors(5*m^2)))
   else t:= 0
   fi;
   m0:= mul(`if`(s[1]=5, s[1]^ceil((s[2]-1)/2),
       s[1]^ceil(s[2]/2)),s=ifactors(n)[2]);
   t + 4 + 8*floor(n/m0/5);
end proc:
df(0):= 1:
ListTools:-PartialSums(map(df,[$0..100])); # Robert Israel, Jun 29 2020