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A155461
a(n) = n^2 + 52*n + 30.
1
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, 4254, 4395
OFFSET
0,1
FORMULA
a(n) = a(n-1) + a(n-2) - a(n-3) + 4 = 3*a(n-1) - 3*a(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)
E.g.f.: (30 + 53*x + x^2)*exp(x). - Elmo R. Oliveira, Oct 19 2024
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
KEYWORD
nonn,easy,changed
AUTHOR
Vincenzo Librandi, Jan 22 2009
EXTENSIONS
Edited by Charles R Greathouse IV, Aug 09 2010
STATUS
approved