A165983 Period 16: repeat 1,1,1,2,1,1,1,2,1,1,1,4,1,1,1,4.

1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1

Offset: 0

Author

Paul Curtz, Oct 03 2009

Keywords

• nonn
• easy
• less

Comments

The numerator of the reduced fraction A061037(n+3)/A061041(2n+6).

Links

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

Crossrefs

Cf. A064038.

Programs

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(( -1-x-x^2-2*x^3-x^8-x^9-x^10-4*x^11 )/((x-1)*(1+x)*(1+x^2)*(x^8+1)))); // G. C. Greubel, Sep 20 2018

Mathematica

LinearRecurrence[{0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1}, {1, 1, 1, 2,  1, 1, 1, 2, 1, 1, 1, 4}, 50] (* G. C. Greubel, Apr 20 2016 *)

PARI

x='x+O('x^50); Vec(( -1-x-x^2-2*x^3-x^8-x^9-x^10-4*x^11 )/((x-1)*(1+x)*(1+x^2)*(x^8+1))) \\ G. C. Greubel, Sep 20 2018

Formula

a(n) = a(n-4) - a(n-8) + a(n-12). - R. J. Mathar, Dec 17 2010

G.f.: ( -1 - x - x^2 - 2*x^3 - x^8 - x^9 - x^10 - 4*x^11 ) / ( (x-1)*(1+x)*(1+x^2)*(x^8+1) ). - R. J. Mathar, Dec 17 2010

a(4n) = a(4n+1) = a(4n+2) = 1. a(4n+3) = A165207(n).