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A109017 a(n) = Kronecker symbol (-6/n).

%I A109017 #29 Feb 16 2025 08:32:58
%S A109017 0,1,0,0,0,1,0,1,0,0,0,1,0,-1,0,0,0,-1,0,-1,0,0,0,-1,0,1,0,0,0,1,0,1,
%T A109017 0,0,0,1,0,-1,0,0,0,-1,0,-1,0,0,0,-1,0,1,0,0,0,1,0,1,0,0,0,1,0,-1,0,0,
%U A109017 0,-1,0,-1,0,0,0,-1,0,1,0,0,0,1,0,1,0,0,0,1,0,-1,0,0,0,-1,0,-1,0,0,0,-1,0,1,0,0,0,1,0,1,0
%N A109017 a(n) = Kronecker symbol (-6/n).
%D A109017 L. B. W. Jolley, Summation of Series, Dover Publications, 1961.
%H A109017 G. C. Greubel, <a href="/A109017/b109017.txt">Table of n, a(n) for n = 0..10000</a>
%H A109017 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KroneckerSymbol.html">Kronecker Symbol</a>
%H A109017 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,0,0,0,-1).
%F A109017 Euler transform of length-24 sequence [ 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1].
%F A109017 a(n) = -a(-n) = a(n+24) for all n in Z.
%F A109017 G.f.: x * (1 + x^6) / (1 - x^4 + x^8).
%F A109017 G.f.: x *(1 -x^8)*(1 -x^12)^2 /((1 -x^4)*(1 -x^6)*(1 -x^24)).
%F A109017 Sum_{n>=1} |a(n)|/n^2 = Pi^2/9 [Jolley equ. 338].
%e A109017 G.f. = x + x^5 + x^7 + x^11 - x^13 - x^17 - x^19 - x^23 + x^25 + x^29 + ...
%p A109017 A109017 := proc(n)
%p A109017         numtheory[jacobi](-6,n) ;
%p A109017 end proc: # _R. J. Mathar_, Nov 03 2011
%t A109017 Table[KroneckerSymbol[-6, n], {n, 0, 104}] (* _Jean-François Alcover_, Jan 10 2014 *)
%o A109017 (PARI) {a(n) = kronecker(-6, n)};
%o A109017 (PARI) {a(n) = (n%2) * (n%3!=0) * (-1)^(n\12)};
%o A109017 (Magma) [KroneckerSymbol(-6,n): n in [0..120]]; // _Vincenzo Librandi_, Aug 09 2015
%K A109017 sign,mult,easy
%O A109017 0,1
%A A109017 _Michael Somos_, Jun 16 2005