A155769 a(n) = 2n^2 + 2n - 41.

-41, -37, -29, -17, -1, 19, 43, 71, 103, 139, 179, 223, 271, 323, 379, 439, 503, 571, 643, 719, 799, 883, 971, 1063, 1159, 1259, 1363, 1471, 1583, 1699, 1819, 1943, 2071, 2203, 2339, 2479, 2623, 2771, 2923, 3079, 3239, 3403, 3571, 3743, 3919, 4099, 4283

Offset

0,1

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.: (-41+86*x-41*x^2)/(1-x)^3. - Vincenzo Librandi, Feb 29 2012

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Feb 29 2012

Sum_{n>=0} 1/a(n) = tan(sqrt(83)*Pi/2)*Pi/(2*sqrt(83)). - Amiram Eldar, Feb 25 2023

Mathematica

CoefficientList[Series[(-41+86x-41x^2)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Feb 29 2012 *)

Prog

(PARI) a(n)=2*n*(n+1)-41 \\ Charles R Greathouse IV, Dec 28 2011
(Magma) I:=[-41, -37, -29]; [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, Feb 29 2012

Crossrefs

Sequence in context: A177996 A217159 A291473 * A247390 A291501 A142719

Adjacent sequences: A155766 A155767 A155768 * A155770 A155771 A155772

Keyword

sign,easy

Author

Vincenzo Librandi, Jan 27 2009

Extensions

Edited by Charles R Greathouse IV, Jul 25 2010

Status

approved