OFFSET
1,1
COMMENTS
Also represents the decimal expansion of 50020080020/9009009009.
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Nov 18 2010
EXTENSIONS
Extended by Ray Chandler, Aug 27 2015
STATUS
approved