A166148 a(n) = (9*n^2 + 9*n - 16)/2.

1, 19, 46, 82, 127, 181, 244, 316, 397, 487, 586, 694, 811, 937, 1072, 1216, 1369, 1531, 1702, 1882, 2071, 2269, 2476, 2692, 2917, 3151, 3394, 3646, 3907, 4177, 4456, 4744, 5041, 5347, 5662, 5986, 6319, 6661, 7012, 7372, 7741, 8119, 8506, 8902, 9307, 9721, 10144

Offset: 1

Author

Vincenzo Librandi, Oct 08 2009

Keywords

• nonn
• easy

Links

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

Programs

Magma

I:=[1, 19, 46]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Mar 15 2012

Mathematica

CoefficientList[Series[(1+16x-8x^2)/(1-x)^3,{x,0,50}],x] (* or *) LinearRecurrence[{3, -3, 1}, {1, 19, 46}, 50] (* Vincenzo Librandi, Mar 15 2012 *)

PARI

a(n)=9*binomial(n+1,2)-8 \\ Charles R Greathouse IV, Jan 11 2012

Formula

a(n) = a(n-1) + 9*n with n > 1, a(1)=1.

From Vincenzo Librandi, Mar 15 2012: (Start)

G.f.: x*(1+16*x-8*x^2)/(1-x)^3.

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

E.g.f.: (1/2)*(9*x^2 + 18*x - 16)*exp(x). - G. C. Greubel, May 01 2016

Sum_{n>=1} 1/a(n) = 1/8 + (2*Pi/(3*sqrt(73)))*tan(sqrt(73)*Pi/6). - Amiram Eldar, Feb 20 2023

Extensions

New name from Charles R Greathouse IV, Jan 11 2012