A242073 a(n) = - (a(n-1)*a(n-4) + a(n-2)*a(n-3)) / a(n-5) with a(0)=1, a(1)=a(2)=-1, a(3)=-2, a(4)=1.

1, -1, -1, -2, 1, -1, -1, 1, 1, 2, -1, 1, 1, -1, -1, -2, 1, -1, -1, 1, 1, 2, -1, 1, 1, -1, -1, -2, 1, -1, -1, 1, 1, 2, -1, 1, 1, -1, -1, -2, 1, -1, -1, 1, 1, 2, -1, 1, 1, -1, -1, -2, 1, -1, -1, 1, 1, 2, -1, 1, 1, -1, -1, -2, 1, -1, -1, 1, 1, 2, -1, 1, 1, -1

Offset

0,4

Comments

Period 12: repeat [1, -1, -1, -2, 1, -1, -1, 1, 1, 2, -1, 1]. - Wesley Ivan Hurt, Aug 29 2014

Links

Antti Karttunen, Table of n, a(n) for n = 0..11999

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

Formula

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

a(2*n+1) = - A057079(n). - Robert Israel, Aug 29 2014

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

G.f.: (1 - x - x^2 - 2*x^3 + x^4 - x^5) / (1 + x^6).

G.f. can be written as 1/(1+x^2) + x*(1+x^2)/(1-x^2+x^4). - Robert Israel, Aug 29 2014

a(n) = ((-1)^(n/2)+(-1)^(3*n/2)+(-1)^((3+n)/6)-(-1)^((3-n)/6)+(-1)^((3-7*n)/6)-(-1)^((3+7*n)/6))/2. - Wesley Ivan Hurt, Jul 21 2015

Example

G.f. = 1 - x - x^2 - 2*x^3 + x^4 - x^5 - x^6 + x^7 + x^8 + 2*x^9 - x^10 + ...

Maple

A242073:=proc(n) option remember;
if n=0 then 1 elif n=1 then -1 elif n=2 then -1 elif n=3 then -2 elif n=4 then 1 elif n=5 then -1 else -A242073(n-6); fi; end:  seq(A242073(n), n=0..100); # Wesley Ivan Hurt, Jul 21 2015

Mathematica

CoefficientList[Series[(1 - x - x^2 - 2 x^3 + x^4 - x^5)/(1 + x^6), {x, 0, 100}], x] (* Wesley Ivan Hurt, Aug 29 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, -1}, {1, -1, -1, -2, 1, -1}, 100] (* Vincenzo Librandi, Jul 22 2015 *)

Prog

(PARI) {a(n) = (-1)^(n\6) * [1, -1, -1, -2, 1, -1][n%6 + 1]};
(Magma) I:=[1, -1, -1, -2, 1, -1]; [n le 6 select I[n] else -Self(n-6): n in [1..100]]; // Vincenzo Librandi, Jul 22 2015

Crossrefs

Cf. A057079.

Sequence in context: A304118 A319679 A364388 * A245477 A319689 A303824

Adjacent sequences: A242070 A242071 A242072 * A242074 A242075 A242076

Keyword

sign,easy

Author

Michael Somos, Aug 14 2014

Status

approved