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A293517 a(n) = A293518(n) - A293519(n); how many more surviving even nodes than surviving (but not bifurcating) odd nodes there are at generation n in the binary tree of persistently squarefree numbers.

%I A293517 #15 Oct 18 2017 08:55:38
%S A293517 0,1,1,1,1,2,1,3,4,5,9,8,10,20,17,36,32,50,66,83,118,171,219,291,410,
%T A293517 511,730,952,1325,1665,2389,3100,4147,5631,7591,10093,13756,18390,
%U A293517 24540,33288,44391,60052,80291,108096,145226,194764,262091,352096,473452,635336,854332,1147668
%N A293517 a(n) = A293518(n) - A293519(n); how many more surviving even nodes than surviving (but not bifurcating) odd nodes there are at generation n in the binary tree of persistently squarefree numbers.
%C A293517 As long as there are at least as many surviving even than surviving (but not bifurcating) odd nodes at each generation in the tree of persistently squarefree numbers (see illustration in A293230), this sequence also stays nonnegative, and being also the first differences of A293441 guarantees its monotonicity. If A293441 is monotonic, then A293230 is also, which in turn implies also that A293430 has infinite number of terms and that there will be nonzero terms arbitrary far in A293233.
%C A293517 The surviving children of even vertices are all of the form 4k+1, while the surviving children (those without an odd sibling) of odd vertices are all of the form 4k+2.
%F A293517 a(n) = A293518(n) - A293519(n).
%F A293517 a(n) = A293441(1+n) - A293441(n).
%o A293517 (Scheme) (define (A293517 n) (- (A293518 n) (A293519 n)))
%Y A293517 Cf. A293230, A293233, A293430, A293518, A293519.
%Y A293517 First differences of A293441.
%Y A293517 Cf. also A293428.
%K A293517 nonn
%O A293517 0,6
%A A293517 _Antti Karttunen_, Oct 16 2017