A109017 - OEIS

A109017

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

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, 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, 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

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OFFSET

0,1

REFERENCES

L. B. W. Jolley, Summation of Series, Dover Publications, 1961.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Kronecker Symbol

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,0,0,0,-1).

FORMULA

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].

a(n) = -a(-n) = a(n+24) for all n in Z.

G.f.: x * (1 + x^6) / (1 - x^4 + x^8).

G.f.: x *(1 -x^8)*(1 -x^12)^2 /((1 -x^4)*(1 -x^6)*(1 -x^24)).

Sum_{n>=1} |a(n)|/n^2 = Pi^2/9 [Jolley equ. 338].

EXAMPLE

G.f. = x + x^5 + x^7 + x^11 - x^13 - x^17 - x^19 - x^23 + x^25 + x^29 + ...

MAPLE

A109017 := proc(n)

numtheory[jacobi](-6, n) ;

end proc: # R. J. Mathar, Nov 03 2011

MATHEMATICA

Table[KroneckerSymbol[-6, n], {n, 0, 104}] (* Jean-François Alcover, Jan 10 2014 *)

PROG

(PARI) {a(n) = kronecker(-6, n)};

(PARI) {a(n) = (n%2) * (n%3!=0) * (-1)^(n\12)};

(Magma) [KroneckerSymbol(-6, n): n in [0..120]]; // Vincenzo Librandi, Aug 09 2015

CROSSREFS

Moebius transform of A192013.

Cf. A296924 (primes not inert in Q(sqrt(-6))), A157437 (primes decomposing), A191059 (prime remaining inert).

Kronecker symbols {(D/n)} for negative fundamental discriminants D = -3..-47, -67, -163: A102283, A101455, A175629, A188510, A011582, A316569, A011585, A289741, A011586, this sequence, A011588, A390614, A388073, A388072, A011591, A011592, A011596, A011615.

Kronecker symbols {(D/n)} for positive fundamental discriminants D = 5..41: A080891, A091337, A110161, A011583, A011584, A322829, A322796, A390615, A011587, A391502, A011589, A391503, A011590.

Sequence in context: A317542 A379275 A322796 * A110161 A134667 A354354

Adjacent sequences: A109014 A109015 A109016 * A109018 A109019 A109020

KEYWORD

sign,mult,easy

AUTHOR

Michael Somos, Jun 16 2005

STATUS

approved