A166150 a(n) = 5*n^2 + 5*n - 9.

1, 21, 51, 91, 141, 201, 271, 351, 441, 541, 651, 771, 901, 1041, 1191, 1351, 1521, 1701, 1891, 2091, 2301, 2521, 2751, 2991, 3241, 3501, 3771, 4051, 4341, 4641, 4951, 5271, 5601, 5941, 6291, 6651, 7021, 7401, 7791, 8191, 8601, 9021, 9451, 9891, 10341

Offset

1,2

Comments

First differences are in A008592.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = a(n-1) + 10*n (with a(1)=1).

G.f.: x*(1+18*x-9*x^2)/(1-x)^3. - Vincenzo Librandi, Sep 13 2013

From G. C. Greubel, May 01 2016: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

E.g.f.: (5*x^2 + 10*x - 9)*exp(x) + 9. (End)

Sum_{n>=1} 1/a(n) = 1/9 + (Pi/sqrt(205))*tan(sqrt(41/5)*Pi/2). - Amiram Eldar, Feb 20 2023

Maple

A166150:=n->5*n^2+5*n-9: seq(A166150(n), n=1..100); # Wesley Ivan Hurt, May 01 2016

Mathematica

Table[(5 n^2 + 5  n - 9), {n, 50}] (* or *) CoefficientList[Series[(1 + 18 x - 9 x^2)/(1 - x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Sep 13 2013 *)
LinearRecurrence[{3, -3, 1}, {1, 21, 51}, 50] (* G. C. Greubel, May 01 2016 *)

Prog

(PARI) a(n)=5*n*(n+1)-9 \\ Charles R Greathouse IV, Jan 11 2012
(Magma) [5*n^2+5*n-9: n in [1..45]]; // Vincenzo Librandi, Sep 13 2013

Crossrefs

Cf. A008592.

Sequence in context: A357679 A235884 A053178 * A224334 A305002 A242236

Adjacent sequences: A166147 A166148 A166149 * A166151 A166152 A166153

Keyword

nonn,easy

Author

Vincenzo Librandi, Oct 08 2009

Extensions

a(29)-a(45) corrected by Charles R Greathouse IV, Jan 11 2012

New name from Charles R Greathouse IV, Jan 11 2012

Status

approved