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

Offset: 0

Author

Michael Somos, Jun 16 2005

Keywords

• sign
• mult
• easy

Examples

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

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).

Programs

Magma

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

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 *)

PARI

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

PARI

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

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].