A217366 a(n) = ((n+6) / gcd(n+6,4)) * (n / gcd(n,4)).

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

Author

Jean-François Alcover, Oct 01 2012

Keywords

• nonn
• easy

Comments

The 6th sequence (p=6) of the family A060819(n)*A060819(n+p).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Crossrefs

Cf. A060819, A181318.

Programs

Magma

[(9-7*(-1)^n)/16*n*(n+6): n in [0..50]]; // G. C. Greubel, Sep 21 2018

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 *)

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

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