A130861 a(n) = (n-1)*(2*n+5).

0, 9, 22, 39, 60, 85, 114, 147, 184, 225, 270, 319, 372, 429, 490, 555, 624, 697, 774, 855, 940, 1029, 1122, 1219, 1320, 1425, 1534, 1647, 1764, 1885, 2010, 2139, 2272, 2409, 2550, 2695, 2844, 2997, 3154, 3315, 3480, 3649, 3822, 3999, 4180, 4365

Offset: 1

Author

Roger L. Bagula, Jul 22 2007

Keywords

• nonn
• easy

Comments

Old name was: "Ratio of Sum of k^2-1 to sum of k made into an integer sequence: (n-1)*(2*n+5)".

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A016838.

Programs

Mathematica

Table[(n-1)(2n+5),{n,50}] (* or *) LinearRecurrence[{3,-3,1},{0,9,22},50] (* Harvey P. Dale, Oct 02 2015 *)

PARI

a(n)=(n-1)*(2*n+5) \\ Charles R Greathouse IV, Sep 24 2015

Formula

a(n) = 3*(n + 1)*( Sum_{k=1..n} k^2-1 )/ ( Sum_{k=1..n} k ) = (-1 + n)*(5 + 2*n).

G.f.: x^2*(9 - 5*x)/(1-x)^3. - R. J. Mathar, Nov 14 2007

a(n) = a(n-1) +4*n +1 for n>1, a(1)=0. - Vincenzo Librandi, Nov 23 2010

a(n) = n*(2n+7) with offset 0. - Michel Marcus, Jan 28 2015

8*a(n) + 49 = A016838(n). - Bruno Berselli, Jan 28 2015

E.g.f.: 5 + (2*x^2 + 5* x -5)*exp(x). - G. C. Greubel, Jul 21 2017