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URL: https://oeis.org/A217366

⇱ A217366 - OEIS

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A217366
a(n) = ((n+6) / gcd(n+6,4)) * (n / gcd(n,4)).
3
0, 7, 2, 27, 5, 55, 9, 91, 14, 135, 20, 187, 27, 247, 35, 315, 44, 391, 54, 475, 65, 567, 77, 667, 90, 775, 104, 891, 119, 1015, 135, 1147, 152, 1287, 170, 1435, 189, 1591, 209, 1755, 230, 1927, 252, 2107, 275, 2295, 299, 2491, 324, 2695, 350, 2907, 377
OFFSET
0,2
COMMENTS
The 6th sequence (p=6) of the family A060819(n)*A060819(n+p).
FORMULA
a(n) = 8^(n mod 2 - 1)*n*(n + 6).
G.f.: x*(7 + 2*x + 6*x^2 - x^3 - 5*x^4)/(1 - x^2)^3. - Bruno Berselli, Oct 01 2012
From Colin Barker, Jan 27 2016: (Start)
a(n) = (9 - 7*(-1)^n)*n*(n + 6)/16.
a(n) = (n^2 + 6*n)/8 for n even.
a(n) = n^2 + 6*n for n odd. (End)
Sum_{n>=1} 1/a(n) = 133/90. - Amiram Eldar, Aug 12 2022
MATHEMATICA
a[n_] := 8^(Mod[n, 2] - 1)*n*(n + 6); Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Oct 01 2012 *)
CoefficientList[Series[x*(7 + 2*x + 6*x^2 - x^3 - 5*x^4)/(1 - x^2)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 15 2012 *)
LinearRecurrence[{0, 3, 0, -3, 0, 1}, {0, 7, 2, 27, 5, 55}, 60] (* Harvey P. Dale, Sep 14 2022 *)
PROG
(PARI) concat(0, Vec(x*(7+2*x+6*x^2-x^3-5*x^4)/((1-x)^3*(1+x)^3) + O(x^100))) \\ Colin Barker, Jan 27 2016
(PARI) vector(50, n, n--; (9-7*(-1)^n)/16*n*(n+6)) \\ G. C. Greubel, Sep 21 2018
(Magma) [(9-7*(-1)^n)/16*n*(n+6): n in [0..50]]; // G. C. Greubel, Sep 21 2018
CROSSREFS
Sequence in context: A269168 A279943 A279999 * A282609 A282450 A389578
KEYWORD
nonn,easy
AUTHOR
STATUS
approved