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

%I A334524 #27 Jul 09 2020 11:58:46
%S A334524 1,5,9,13,17,29,33,37,41,45,65,69,73,77,81,101,105,109,113,117,153,
%T A334524 157,161,165,169,181,185,189,193,197,233,237,241,245,249,261,273,277,
%U A334524 281,285,321,325,329,333,337,373,377,381,385,397,417,421,425,429,433,445
%N A334524 Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w^2 + 5xy = 0.
%C A334524 If n is squarefree and not divisible by 5, a(n) = a(n-1)+4. - _Robert Israel_, Jun 29 2020
%H A334524 Brandon Crofts, <a href="/A334524/b334524.txt">Table of n, a(n) for n = 0..20000</a> (first 10001 terms from Robert Israel)
%H A334524 Brandon Crofts, <a href="/A334524/a334524.txt">Mathematica code for 334524</a>
%p A334524 df:= proc(n) local t,s,m0,m;
%p A334524    if n mod 5 = 0 then
%p A334524      m:= n/5;
%p A334524      t:= 4*nops(select(s -> s < n and s > m, numtheory:-divisors(5*m^2)))
%p A334524    else t:= 0
%p A334524    fi;
%p A334524    m0:= mul(`if`(s[1]=5, s[1]^ceil((s[2]-1)/2),
%p A334524        s[1]^ceil(s[2]/2)),s=ifactors(n)[2]);
%p A334524    t + 4 + 8*floor(n/m0/5);
%p A334524 end proc:
%p A334524 df(0):= 1:
%p A334524 ListTools:-PartialSums(map(df,[$0..100])); # _Robert Israel_, Jun 29 2020
%Y A334524 Cf. A211423.
%K A334524 nonn
%O A334524 0,2
%A A334524 _Brandon Crofts_, Jun 15 2020