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

%I A334525 #18 Jul 01 2020 20:24:10
%S A334525 1,5,9,13,17,21,25,37,41,45,49,53,57,61,81,85,89,93,97,101,105,125,
%T A334525 129,133,137,141,145,149,185,189,193,197,201,205,209,229,233,237,241,
%U A334525 245,249,253,297,301,305,309,313,317,321,333,337,341,345,349,353,357,393,397
%N A334525 Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w^2 + 7xy = 0.
%C A334525 If n is squarefree and not divisible by 7, a(n) = a(n-1)+4. - _Robert Israel_, Jul 01 2020
%H A334525 Brandon Crofts, <a href="/A334525/b334525.txt">Table of n, a(n) for n = 0..20000</a>
%H A334525 Brandon Crofts, <a href="/A334525/a334525.txt">Mathematica code for A334525</a>
%p A334525 df:= proc(n) local t, s, m0, m;
%p A334525    if n mod 7 = 0 then
%p A334525      m:= n/7;
%p A334525      t:= 4*nops(select(s -> s < n and s > m, numtheory:-divisors(7*m^2)))
%p A334525    else t:= 0
%p A334525    fi;
%p A334525    m0:= mul(`if`(s[1]=7, s[1]^ceil((s[2]-1)/2),
%p A334525        s[1]^ceil(s[2]/2)), s=ifactors(n)[2]);
%p A334525    t + 4 + 8*floor(n/m0/7);
%p A334525 end proc:
%p A334525 df(0):= 1:
%p A334525 ListTools:-PartialSums(map(df, [$0..100])); # _Robert Israel_, Jul 01 2020
%Y A334525 Cf. A211423.
%K A334525 nonn
%O A334525 0,2
%A A334525 _Brandon Crofts_, Jun 15 2020