A166154 a(n) = 7*n*(n+1)/2 - 5.

2, 16, 37, 65, 100, 142, 191, 247, 310, 380, 457, 541, 632, 730, 835, 947, 1066, 1192, 1325, 1465, 1612, 1766, 1927, 2095, 2270, 2452, 2641, 2837, 3040, 3250, 3467, 3691, 3922, 4160, 4405, 4657, 4916, 5182, 5455, 5735, 6022, 6316, 6617, 6925, 7240, 7562

Offset

1,1

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) = A166146(n)+1.

a(n) = a(n-1)+7*n = 3*a(n-1) -3*a(n-2) +a(n-3).

G.f.: x*(-2-10*x+5*x^2)/(x-1)^3.

E.g.f.: (7/2)*((x^2 + 2*x - 5)*exp(x) + 5). - G. C. Greubel, May 01 2016

Sum_{n>=1} 1/a(n) = 1/5 + (2*Pi/sqrt(329))*tan(sqrt(47/7)*Pi/2). - Amiram Eldar, Feb 20 2023

Mathematica

Table[7 n (n + 1)/2 - 5, {n, 100}] (* or *) CoefficientList[Series[(- 2 - 10 x + 5 x^2) / (x - 1)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Sep 13 2013 *)
LinearRecurrence[{3, -3, 1}, {2, 16, 37}, 50] (* G. C. Greubel, May 01 2016 *)

Prog

(Magma) [7*n*(n+1)/2-5: n in [1..50]]; // Vincenzo Librandi, Sep 13 2013
(PARI) a(n)=7*n*(n+1)/2-5 \\ Charles R Greathouse IV, May 02 2016

Crossrefs

Cf. A166146.

Sequence in context: A019064 A123135 A327542 * A034507 A211620 A023638

Adjacent sequences: A166151 A166152 A166153 * A166155 A166156 A166157

Keyword

nonn,easy

Author

Vincenzo Librandi, Oct 08 2009

Extensions

Definition replaced by polynomial, A-number corrected, formulas added by R. J. Mathar, Oct 12 2009

Status

approved