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A181668 Period 12: repeat [5,5,5,2,2,2,8,8,8,2,2,2]. 1
5, 5, 5, 2, 2, 2, 8, 8, 8, 2, 2, 2, 5, 5, 5, 2, 2, 2, 8, 8, 8, 2, 2, 2, 5, 5, 5, 2, 2, 2, 8, 8, 8, 2, 2, 2, 5, 5, 5, 2, 2, 2, 8, 8, 8, 2, 2, 2, 5, 5, 5, 2, 2, 2, 8, 8, 8, 2, 2, 2, 5, 5, 5, 2, 2, 2, 8, 8, 8, 2, 2, 2, 5, 5, 5, 2, 2, 2, 8, 8, 8, 2, 2, 2, 5, 5, 5, 2, 2, 2, 8, 8, 8, 2, 2, 2, 5, 5, 5, 2, 2, 2, 8, 8, 8, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also represents the decimal expansion of 50020080020/9009009009.

LINKS

Table of n, a(n) for n=1..108.

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

FORMULA

From R. J. Mathar, Feb 04 2011: (Start)

a(n) = a(n-1) - a(n-3) + a(n-4) - a(n-6) + a(n-7) - a(n-9) + a(n-10).

G.f.: x*(5 + 2*x^3 + 8*x^6 + 2*x^9) / ( (1-x)*(1+x)*(x^2+1)*(x^2 - x + 1)*(x^4 - x^2 + 1) ). (End)

Let b(n) = A061037(n+1) - 2*A061037(n) + A061037(n-1) denote the second differences of A061037. Then a(n+2) = b(n) mod 9. - Paul Curtz, Mar 02 2011

a(n) = (17 - 9*cos(t)^2 - 6*sin(t) + 9*sin(t)^2)/4, where t := Pi*(3*n + 3 - sqrt(3)*sin(2*Pi*(n + 1)/3) + sqrt(3)*sin(4*Pi*(n + 1)/3))/18. - Wesley Ivan Hurt, Sep 26 2018

MATHEMATICA

LinearRecurrence[{1, 0, -1, 1, 0, -1, 1, 0, -1, 1}, {5, 5, 5, 2, 2, 2, 8, 8, 8, 2}, 108] (* Ray Chandler, Aug 27 2015 *)

CoefficientList[Series[x*(5+2*x^3+8*x^6+2*x^9)/((1-x)*(1+x)*(x^2+1)*(x^2-x+1)*(x^4-x^2+1)), {x, 0, 50}], x] (* G. C. Greubel, Sep 20 2018 *)

PadRight[{}, 120, {5, 5, 5, 2, 2, 2, 8, 8, 8, 2, 2, 2}] (* Harvey P. Dale, Jul 03 2021 *)

PROG

(PARI) x='x+O('x^50); Vec(x*(5+2*x^3+8*x^6+2*x^9)/((1-x)*(1+x)*(x^2+1)*(x^2-x+1)*(x^4-x^2+1))) \\ G. C. Greubel, Sep 20 2018

(MAGMA) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(5+2*x^3+8*x^6+2*x^9)/((1-x)*(1+x)*(x^2+1)*(x^2-x+1)*(x^4-x^2+1)))); // G. C. Greubel, Sep 20 2018

CROSSREFS

Cf. A061037.

Sequence in context: A172359 A093796 A021647 * A247824 A094851 A173602

Adjacent sequences:  A181665 A181666 A181667 * A181669 A181670 A181671

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Nov 18 2010

EXTENSIONS

Extended by Ray Chandler, Aug 27 2015

STATUS

approved

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Last modified July 29 11:46 EDT 2021. Contains 346344 sequences. (Running on oeis4.)