A260192 Kronecker symbol(-6 / 2*n + 7).

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

G. C. Greubel, Table of n, a(n) for n = 0..1000

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, -1, 0, 0, 0, 0, 0, 1].

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

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

a(n) = = (-1)^n * A260190(n) = A117441(n+1) = A109017(2*n + 7).

a(2*n) = A010892(n). a(2*n + 1) = A128834(n). a(3*n + 1) = 0. a(3*n) = a(3*n + 2) = A087960(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 + 7];
LinearRecurrence[{0, 1, 0, -1}, {1, 0, 1, -1}, 50] (* G. C. Greubel, Jan 15 2018 *)
CoefficientList[Series[(1-x^3)/(1-x^2+x^4), {x, 0, 100}], x] (* Harvey P. Dale, Jun 30 2021 *)

Prog

(PARI) {a(n) = kronecker( -6, 2*n + 7)};
(PARI) {a(n) = (-1)^(n\6 + n) * [1, 0, 1][n%3 + 1]};
(PARI) {a(n) = if( n<0, n=-1-n); polcoeff( (1 - x^3) / (1 - x^2 + x^4) + x * O(x^n), n)};
(Magma) I:=[1, 0, 1, -1]; [n le 4 select I[n] else Self(n-2) - Self(n-4): n in [1..30]]; // G. C. Greubel, Jan 15 2018

Crossrefs

Cf. A087960, A109017, A128834, A260190.

Essentially the same as A117441.

Sequence in context: A141687 A305385 A260190 * A057078 A204418 A127245

Adjacent sequences: A260189 A260190 A260191 * A260193 A260194 A260195

Keyword

sign,easy

Author

Michael Somos, Jul 18 2015

Status

approved