A286390 a(n) = a(n-2) - 2*a(n-3) + a(n-4) for n>3, a(0)=0, a(1)=2, a(2)=-1, a(3)=3.

0, 2, -1, 3, -5, 7, -12, 20, -31, 51, -83, 133, -216, 350, -565, 915, -1481, 2395, -3876, 6272, -10147, 16419, -26567, 42985, -69552, 112538, -182089, 294627, -476717, 771343, -1248060, 2019404, -3267463, 5286867, -8554331, 13841197, -22395528, 36236726

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,1,-2,1).

Formula

a(n) = A286311(-n).

b(n) = A286311(n) + (period 6 sequence : repeat [0, 1, 0, 0, 0, -1]) = 0, 2, 1, 3, 5, 7, 12, 20, 31, 51, 83, 133, ... . See A134667(n).

a(n) = -(-1)^n*b(n).

G.f.: x*(2 - x + x^2) / ((1 + x - x^2)*(1 - x + x^2)). - Colin Barker, May 08 2017

Mathematica

LinearRecurrence[{0, 1, -2, 1}, {0, 2, -1, 3}, 38] (* or *)
CoefficientList[Series[x (2 - x + x^2)/((1 + x - x^2) (1 - x + x^2)), {x, 0, 37}], x] (* Michael De Vlieger, May 08 2017 *)

Prog

(PARI) concat(0, Vec(x*(2 - x + x^2) / ((1 + x - x^2)*(1 - x + x^2)) + O(x^60))) \\ Colin Barker, May 08 2017

Crossrefs

Cf. A134667, A286311.

Sequence in context: A075643 A076074 A319153 * A135017 A070168 A246646

Adjacent sequences: A286387 A286388 A286389 * A286391 A286392 A286393

Keyword

sign,easy

Author

Paul Curtz, May 08 2017

Extensions

Typo in data fixed and more terms added by Colin Barker, May 08 2017

Status

approved