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%I #14 Jun 24 2018 18:08:45
%S 1,0,1,1,0,1,-1,0,-1,-1,0,-1,1,0,1,1,0,1,-1,0,-1,-1,0,-1,1,0,1,1,0,1,
%T -1,0,-1,-1,0,-1,1,0,1,1,0,1,-1,0,-1,-1,0,-1,1,0,1,1,0,1,-1,0,-1,-1,0,
%U -1,1,0,1,1,0,1,-1,0,-1,-1,0,-1,1,0,1,1,0,1
%N Kronecker symbol(-6 / 2*n + 1).
%H Seiichi Manyama, <a href="/A260190/b260190.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,-1).
%F Euler transform of length 12 sequence [ 0, 1, 1, -1, 0, -2, 0, 0, 0, 0, 0, 1].
%F G.f.: (1 + x^3) / (1 - x^2 + x^4).
%F G.f.: 1 / (1 - x^2 / (1 - x / (1 + 2*x / ( 1 - x / (1 - x / (1 + x)))))).
%F a(n) = (-1)^n * a(n+3) = -a(n+6) = a(5-n) = a(n+2) - a(n+4) for all n in Z.
%F a(n) = A117441(n-2) = (-1)^n * A260192(n) = (-1)^n * A117441(n+1) = A109017(2*n + 1). a(n) + a(n+1) = A214438(n-1).
%F a(2*n) = A010892(n). a(3*n + 1) = 0. a(3*n) = a(3*n + 2) = A057077(n).
%e G.f. = 1 + x^2 + x^3 + x^5 - x^6 - x^8 - x^9 - x^11 + x^12 + x^14 + x^15 + ...
%t a[ n_] := KroneckerSymbol[ -6, 2 n + 1];
%t LinearRecurrence[{0,1,0,-1},{1,0,1,1},120] (* _Harvey P. Dale_, Jun 24 2018 *)
%o (PARI) {a(n) = kronecker( -6, 2*n + 1)};
%o (PARI) {a(n) = (-1)^(n\6) * [ 1, 0, 1][n%3 + 1]};
%o (PARI) {a(n) = if( n<3, n=5-n); polcoeff( (1 + x^3) / (1 - x^2 + x^4) + x * O(x^n), n)};
%Y Cf. A010892, A057077, A109017, A117441, A214438, A260192.
%K sign,easy
%O 0
%A _Michael Somos_, Jul 18 2015
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