A166144 a(n) = (11*n^2 + 11*n - 20)/2.

1, 23, 56, 100, 155, 221, 298, 386, 485, 595, 716, 848, 991, 1145, 1310, 1486, 1673, 1871, 2080, 2300, 2531, 2773, 3026, 3290, 3565, 3851, 4148, 4456, 4775, 5105, 5446, 5798, 6161, 6535, 6920, 7316, 7723, 8141, 8570, 9010, 9461, 9923, 10396, 10880

Offset: 1

Author

Vincenzo Librandi, Oct 16 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, 23, 56]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Mar 15 2012

Mathematica

CoefficientList[Series[(1+20x-10x^2)/(1-x)^3,{x,0,50}],x] (* or *) LinearRecurrence[{3, -3, 1}, {1, 23, 56}, 50] (* Vincenzo Librandi, Mar 15 2012 *)
Table[(11 n^2 + 11 n - 20)/2, {n, 44}] (* Michael De Vlieger, Apr 27 2016 *)

PARI

a(n)=11*binomial(n+1,2)-10 \\ Charles R Greathouse IV, Jan 11 2012

Formula

a(n) = a(n-1) + 11*n, a(1)=1, with n>1.

From Vincenzo Librandi, Mar 15 2012: (Start)

G.f.: x*(1+20*x-10*x^2)/(1-x)^3.

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

E.g.f.: (1/2)*(-20 + 22*x + 11*x^2)*exp(x). - G. C. Greubel, Apr 26 2016

Sum_{n>=1} 1/a(n) = 1/10 + (2*Pi/sqrt(1001))*tan(sqrt(91/11)*Pi/2). - Amiram Eldar, Feb 20 2023

Extensions

New name from Charles R Greathouse IV, Jan 11 2012