A174338 a(n) = 97*n^2.

0, 97, 388, 873, 1552, 2425, 3492, 4753, 6208, 7857, 9700, 11737, 13968, 16393, 19012, 21825, 24832, 28033, 31428, 35017, 38800, 42777, 46948, 51313, 55872, 60625, 65572, 70713, 76048, 81577, 87300, 93217, 99328, 105633, 112132, 118825

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.: 97*x*(1+x)/(1-x)^3. - Vincenzo Librandi, Feb 25 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 25 2012

a(n) = (49n)^2 - (48n)^2 = (9n)^2 + (4n)^2. - Vincenzo Librandi, Feb 25 2012

Mathematica

CoefficientList[Series[97*x*(x+1)/(1-x)^3, {x, 0, 33}], x] (* Vincenzo Librandi, Feb 25 2012 *)
97*Range[0, 40]^2 (* or *) LinearRecurrence[{3, -3, 1}, {0, 97, 388}, 40] (* Harvey P. Dale, Mar 12 2022 *)

Prog

(Magma) [97*n^2: n in [0..50]]; /* or */ I:=[0, 97, 388]; [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 25 2012
(PARI) a(n)=97*n^2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Sequence in context: A366352 A105128 A031927 * A050666 A160440 A107213

Adjacent sequences: A174335 A174336 A174337 * A174339 A174340 A174341

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 16 2010

Status

approved