A063942 Follow k with k-1 and k-2.

1, 0, -1, 2, 1, 0, 3, 2, 1, 4, 3, 2, 5, 4, 3, 6, 5, 4, 7, 6, 5, 8, 7, 6, 9, 8, 7, 10, 9, 8, 11, 10, 9, 12, 11, 10, 13, 12, 11, 14, 13, 12, 15, 14, 13, 16, 15, 14, 17, 16, 15, 18, 17, 16, 19, 18, 17, 20, 19, 18, 21, 20, 19, 22, 21, 20, 23, 22, 21, 24, 23, 22, 25, 24, 23, 26, 25, 24, 27, 26, 25, 28, 27, 26, 29, 28, 27, 30, 29, 28, 31, 30, 29, 32

Offset

0,4

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: ( 1-x^2+2*x^3-x ) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Jul 14 2015

a(3n) = n+1. a(3n+1) = n. a(3n+2) = n-1. - R. J. Mathar, Jan 10 2017

a(n) = (3*n-3-12*cos(2*(n-5)*Pi/3)+4*sqrt(3)*sin(2*(n-5)*Pi/3))/9. - Wesley Ivan Hurt, Sep 29 2017

E.g.f.: exp(x)*(x - 1)/3 + 4*exp(-x/2)*(3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2))/9. - Stefano Spezia, Oct 02 2022

Sum_{n>=6} (-1)^n/a(n) = 3*(log(2)-1/2). - Amiram Eldar, Oct 04 2022

Mathematica

LinearRecurrence[{1, 0, 1, -1}, {1, 0, -1, 2}, 100] (* Amiram Eldar, Oct 04 2022 *)

Prog

(PARI) a(n) = (n\3)-(n%3)+1

Crossrefs

Cf. A028242.

Sequence in context: A176095 A295508 A260672 * A263405 A106384 A333119

Adjacent sequences: A063939 A063940 A063941 * A063943 A063944 A063945

Keyword

easy,sign,changed

Author

Jason Earls, Sep 01 2001

Status

approved