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

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: (1+2*x+7*x^2)/(1-x)^3. - Vincenzo Librandi, Jul 06 2012

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jul 06 2012

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

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 *)

Prog

(Magma) [ 5*n^2-n+1: n in [0..50] ];
(PARI) a(n)=5*n^2-n+1 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A005476.

Sequence in context: A022267 A094465 A020580 * A146616 A146395 A154302

Adjacent sequences: A172040 A172041 A172042 * A172044 A172045 A172046

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 29 2010

Extensions

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

Status

approved