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a(0) = 0; and for n > 0, a(n) = a(n-1) + (A008966(4n-1) - A008966(4n+1)).
3

%I #13 Oct 16 2017 19:58:54

%S 0,0,1,1,1,1,2,1,1,1,1,2,3,3,3,3,2,2,2,1,2,2,2,2,2,1,1,1,1,2,3,4,4,4,

%T 3,3,3,2,3,3,3,3,4,3,2,2,2,3,3,3,3,3,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,

%U 4,3,2,2,3,3,4,4,4,4,4,3,3,4,4,5,5,5,4,4,3,3,4,3,4,4,3,3,3,2,2,2,2,3,3,3,3,3

%N a(0) = 0; and for n > 0, a(n) = a(n-1) + (A008966(4n-1) - 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+1. See A293229 for another version.

%C The first negative term is a(4014) = -1.

%H Antti Karttunen, <a href="/A293429/b293429.txt">Table of n, a(n) for n = 0..11111</a>

%H Hans Havermann, <a href="/A293429/a293429.png">Plot of n, a(n) for n = 0..200000</a>

%F a(0) = 0; and for n > 0, a(n) = a(n-1) + (A008966(4n-1) - A008966(4n+1)).

%o (Scheme, with memoization-macro definec)

%o (definec (A293429 n) (if (zero? n) n (+ (- (A008966 (+ -1 (* 4 n))) (A008966 (+ 1 (* 4 n)))) (A293429 (- n 1)))))

%Y Cf. A008966, A293229 (a variant).

%K sign

%O 0,7

%A _Antti Karttunen_, Oct 16 2017