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A165983 Period 16: repeat 1,1,1,2,1,1,1,2,1,1,1,4,1,1,1,4. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..104.

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(n) = (1/80)*(16*(n mod 16) - 14*((n+1) mod 16) + ((n+2) mod 16) + ((n+3) mod 16) + 16*((n+4) mod 16) - 14*((n+5) mod 16) + ((n+6) mod 16) + ((n+7) mod 16) + 6*((n+8) mod 16) - 4*((n+9) mod 16) + ((n+10) mod 16) + ((n+11) mod 16) + 6*((n+12) mod 16) - 4*((n+13) mod 16) + ((n+14) mod 16) + ((n+15) mod 16)), with n >= 0. - Paolo P. Lava, Oct 19 2009

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

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 *)

PROG

(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

(MAGMA) m:=50; R<x>:=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

CROSSREFS

Cf. A064038.

Sequence in context: A161096 A214247 A211987 * A300719 A083894 A128257

Adjacent sequences:  A165980 A165981 A165982 * A165984 A165985 A165986

KEYWORD

nonn,easy,less

AUTHOR

Paul Curtz, Oct 03 2009

STATUS

approved

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Last modified July 9 18:08 EDT 2020. Contains 335545 sequences. (Running on oeis4.)