A260190 Kronecker symbol(-6 / 2*n + 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, 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, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1

Offset

0

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

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

Formula

Euler transform of length 12 sequence [ 0, 1, 1, -1, 0, -2, 0, 0, 0, 0, 0, 1].

G.f.: (1 + x^3) / (1 - x^2 + x^4).

G.f.: 1 / (1 - x^2 / (1 - x / (1 + 2*x / ( 1 - x / (1 - x / (1 + x)))))).

a(n) = (-1)^n * a(n+3) = -a(n+6) = a(5-n) = a(n+2) - a(n+4) for all n in Z.

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).

a(2*n) = A010892(n). a(3*n + 1) = 0. a(3*n) = a(3*n + 2) = A057077(n).

Example

G.f. = 1 + x^2 + x^3 + x^5 - x^6 - x^8 - x^9 - x^11 + x^12 + x^14 + x^15 + ...

Mathematica

a[ n_] := KroneckerSymbol[ -6, 2 n + 1];
LinearRecurrence[{0, 1, 0, -1}, {1, 0, 1, 1}, 120] (* Harvey P. Dale, Jun 24 2018 *)

Prog

(PARI) {a(n) = kronecker( -6, 2*n + 1)};
(PARI) {a(n) = (-1)^(n\6) * [ 1, 0, 1][n%3 + 1]};
(PARI) {a(n) = if( n<3, n=5-n); polcoeff( (1 + x^3) / (1 - x^2 + x^4) + x * O(x^n), n)};

Crossrefs

Cf. A010892, A057077, A109017, A117441, A214438, A260192.

Sequence in context: A174208 A141687 A305385 * A260192 A057078 A204418

Adjacent sequences: A260187 A260188 A260189 * A260191 A260192 A260193

Keyword

sign,easy

Author

Michael Somos, Jul 18 2015

Status

approved