A172043 a(n) = 5*n^2 - n + 1.

1, 5, 19, 43, 77, 121, 175, 239, 313, 397, 491, 595, 709, 833, 967, 1111, 1265, 1429, 1603, 1787, 1981, 2185, 2399, 2623, 2857, 3101, 3355, 3619, 3893, 4177, 4471, 4775, 5089, 5413, 5747, 6091, 6445, 6809, 7183, 7567, 7961, 8365, 8779, 9203, 9637, 10081, 10535

Offset: 0

Author

Vincenzo Librandi, Jan 29 2010

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A005476.

Programs

Magma

[ 5*n^2-n+1: n in [0..50] ];

Mathematica

CoefficientList[Series[(7*x^2+2*x+1)/(1-x)^3,{x,0,40}],x] (* Vincenzo Librandi, Jul 06 2012 *)
Table[5n^2-n+1,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{1,5,19},50] (* Harvey P. Dale, Aug 06 2022 *)

PARI

a(n)=5*n^2-n+1 \\ Charles R Greathouse IV, Jun 17 2017

Formula

From Vincenzo Librandi, Jul 06 2012: (Start)

G.f.: (1+2*x+7*x^2)/(1-x)^3.

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

a(n) = 2*A005476(n) + 1. - Bruno Berselli, Jul 06 2012

E.g.f.: exp(x)*(1 + 4*x + 5*x^2). - Elmo R. Oliveira, Oct 31 2024

Extensions

Replaced definition with formula. - N. J. A. Sloane, Mar 03 2010