A101677 a(n) = a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6).

1, 1, -1, -2, -2, -2, -1, -1, -3, -4, -4, -4, -3, -3, -5, -6, -6, -6, -5, -5, -7, -8, -8, -8, -7, -7, -9, -10, -10, -10, -9, -9, -11, -12, -12, -12, -11, -11, -13, -14, -14, -14, -13, -13, -15, -16, -16, -16, -15, -15, -17, -18, -18, -18, -17, -17, -19, -20, -20, -20, -19, -19, -21, -22, -22, -22, -21, -21, -23, -24, -24, -24, -23, -23, -25, -26, -26, -26, -25, -25, -27

Offset

0,4

Comments

Partial sums of A101676, second partial sums of A101675.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

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

Formula

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

a(n) = 2*sqrt(3)*sin(2*Pi*n/3)/9 + cos(Pi*n/3) + sin(Pi*n/3)/sqrt(3) - n/3.

a(3*(n+1)) = -A014681(n+1); a(3*n) = a(3*n+1) = 0^n -A014681(n); a(3*n+2) = -(n+1).

Mathematica

LinearRecurrence[{2, -2, 2, -2, 2, -1}, {1, 1, -1, -2, -2, -2}, 81] (* Ray Chandler, Sep 03 2015 *)
CoefficientList[Series[(1-x-x^2)/((1-x)^2(1+x^2+x^4)), {x, 0, 80}], x] (* Harvey P. Dale, Dec 02 2021 *)

Prog

(PARI) x='x+O('x^100); Vec((1-x-x^2)/((1-x)^2*(1+x^2+x^4))) \\ G. C. Greubel, Sep 07 2018
(Magma) m:=100; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x-x^2)/((1-x)^2*(1+x^2+x^4)))); // G. C. Greubel, Sep 07 2018

Crossrefs

Sequence in context: A118400 A159853 A087698 * A364366 A152067 A286756

Adjacent sequences: A101674 A101675 A101676 * A101678 A101679 A101680

Keyword

easy,sign

Author

Paul Barry, Dec 11 2004

Status

approved