A155461 a(n) = n^2 + 52*n + 30.

30, 83, 138, 195, 254, 315, 378, 443, 510, 579, 650, 723, 798, 875, 954, 1035, 1118, 1203, 1290, 1379, 1470, 1563, 1658, 1755, 1854, 1955, 2058, 2163, 2270, 2379, 2490, 2603, 2718, 2835, 2954, 3075, 3198, 3323, 3450, 3579, 3710, 3843, 3978, 4115

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

a(n) = a(n-1) + a(n-2) - a(n-3) + 4 = 3a(n-1) - 3a(n-2) + a(n-3).

From Vincenzo Librandi, Feb 26 2012: (Start)

G.f.: (30 - 7*x - 21*x^2)/(1-x)^3.

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

From Amiram Eldar, May 06 2023: (Start)

Sum_{n>=-26} 1/a(n) = -1/1292 - cot(sqrt(646)*Pi)*Pi/(2*sqrt(646)).

Sum_{n>=-26} (-1)^n/a(n) = -1/1292 - cosec(sqrt(646)*Pi)*Pi/(2*sqrt(646)). (End)

Mathematica

LinearRecurrence[{3, -3, 1}, {30, 83, 138}, 50] (* or *) CoefficientList[Series[(-21x^2-7x+30)/(1-x)^3, {x, 0, 60}], x] (* Vincenzo Librandi, Feb 26 2012 *)

Prog

(Magma) I:=[30, 83, 138]; [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 26 2012
(PARI) for(n=0, 50, print1(n^2 + 52*n + 30", ")); \\ Vincenzo Librandi, Feb 26 2012

Crossrefs

Sequence in context: A044168 A044549 A353176 * A165772 A277980 A241025

Adjacent sequences: A155458 A155459 A155460 * A155462 A155463 A155464

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 22 2009

Extensions

Edited by Charles R Greathouse IV, Aug 09 2010

Status

approved