A166593 Partial sums of A166592.
0, 1, 4, 6, 9, 10, 10, 9, 6, 4, 1, 0, 0, 1, 4, 6, 9, 10, 10, 9, 6, 4, 1, 0, 0, 1, 4, 6, 9, 10, 10, 9, 6, 4, 1, 0, 0, 1, 4, 6, 9, 10, 10, 9, 6, 4, 1, 0, 0, 1, 4, 6, 9, 10, 10, 9, 6, 4, 1, 0, 0, 1, 4, 6, 9, 10, 10, 9, 6, 4, 1, 0, 0, 1, 4, 6, 9, 10, 10, 9, 6, 4, 1, 0, 0, 1, 4, 6, 9, 10, 10, 9, 6, 4, 1, 0, 0
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1,-1,1).
Programs
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Mathematica
LinearRecurrence[{1,1,-1,-1,1}, {0,1,4,6,9}, 25] (* G. C. Greubel, May 18 2016 *)
Formula
G.f.: x(1+3x+x^2)/((1-x)(1-x^2+x^4)) = x(1+3x+x^2)/(1-x-x^2+x^3+x^4-x^5).
a(n) = a(n-1) + a(n-2) - a(n-3) - a(n-4) + a(n-5).
a(n) = (sqrt(8) - sqrt(6))*cos(5*Pi*n/6 + 5*Pi/12)-(sqrt(8) + sqrt(6))*cos(Pi*n/6 + Pi/12) + 5.
a(n + 12) = a(n). - G. C. Greubel, May 18 2016