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Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w^2 + 7xy = 0.
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%I #18 Jul 01 2020 20:24:10

%S 1,5,9,13,17,21,25,37,41,45,49,53,57,61,81,85,89,93,97,101,105,125,

%T 129,133,137,141,145,149,185,189,193,197,201,205,209,229,233,237,241,

%U 245,249,253,297,301,305,309,313,317,321,333,337,341,345,349,353,357,393,397

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

%C If n is squarefree and not divisible by 7, a(n) = a(n-1)+4. - _Robert Israel_, Jul 01 2020

%H Brandon Crofts, <a href="/A334525/b334525.txt">Table of n, a(n) for n = 0..20000</a>

%H Brandon Crofts, <a href="/A334525/a334525.txt">Mathematica code for A334525</a>

%p df:= proc(n) local t, s, m0, m;

%p if n mod 7 = 0 then

%p m:= n/7;

%p t:= 4*nops(select(s -> s < n and s > m, numtheory:-divisors(7*m^2)))

%p else t:= 0

%p fi;

%p m0:= mul(`if`(s[1]=7, s[1]^ceil((s[2]-1)/2),

%p s[1]^ceil(s[2]/2)), s=ifactors(n)[2]);

%p t + 4 + 8*floor(n/m0/7);

%p end proc:

%p df(0):= 1:

%p ListTools:-PartialSums(map(df, [$0..100])); # _Robert Israel_, Jul 01 2020

%Y Cf. A211423.

%K nonn

%O 0,2

%A _Brandon Crofts_, Jun 15 2020