%I #18 Oct 16 2017 19:58:17
%S 0,0,1,1,1,1,1,1,1,1,1,2,3,3,3,2,2,2,1,1,2,2,2,2,1,1,1,1,1,2,3,4,4,3,
%T 3,3,2,2,3,3,3,3,3,2,2,2,2,3,3,3,3,2,2,2,2,2,3,3,3,3,2,3,3,3,3,4,4,4,
%U 3,2,2,2,3,3,4,4,4,4,3,3,3,4,4,5,5,4,4,3,3,3,3,3,4,3,3,3,2,2,2,2,2,3,3,3,3,2
%N a(0) = 0; and for n > 0, a(n) = a(n-1) + (A008966(4n+3) - A008966(4n+1)).
%C The sequence indicates about a possible bias (or lack of it) in the distribution of squarefree numbers among the numbers of the form 4k+1 vs. the numbers of the form 4k+3. See A293429 for another version.
%C The first negative term is a(1702) = -1.
%H Antti Karttunen, <a href="/A293229/b293229.txt">Table of n, a(n) for n = 0..10000</a>
%H Hans Havermann, <a href="/A293229/a293229.png">Plot of n, a(n) for n = 0..200000</a>
%H Hans Havermann, <a href="/A293229/a293229_1.png">Plot of n, a(n) for n = 0..10^7</a>
%F a(0) = 0; and for n > 0, a(n) = a(n-1) + (A008966(4n+3) - A008966(4n+1)).
%o (PARI) up_to = 10000; bias = 0; for(k=0,up_to,bias += (issquarefree((4*k)+3)-issquarefree((4*k)+1)); write("b293229.txt", k, " ", bias));
%o (Scheme, with memoization-macro definec)
%o (definec (A293229 n) (if (zero? n) n (+ (- (A008966 (+ 3 (* 4 n))) (A008966 (+ 1 (* 4 n)))) (A293229 (- n 1)))))
%Y Cf. A008966, A293428, A293429 (a variant).
%K sign
%O 0,12
%A _Antti Karttunen_, Oct 12 2017