A144314 a(n) = 3*n*(6*n + 1).

0, 21, 78, 171, 300, 465, 666, 903, 1176, 1485, 1830, 2211, 2628, 3081, 3570, 4095, 4656, 5253, 5886, 6555, 7260, 8001, 8778, 9591, 10440, 11325, 12246, 13203, 14196, 15225, 16290, 17391, 18528, 19701, 20910, 22155, 23436, 24753, 26106, 27495

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = A000217(6*n) = A014105(3*n) = A081266(2*n).

G.f.: 3*x*(7+5*x)/(1-x)^3. - Vincenzo Librandi, Dec 18 2014

From Wesley Ivan Hurt, Dec 16 2015: (Start)

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

a(n) = 3 * A049453(n). (End)

E.g.f.: 3*exp(x)*x*(7 + 6*x). - Stefano Spezia, Jun 29 2021

Maple

A144314:=n->3*n*(6*n+1): seq(A144314(n), n=0..70); # Wesley Ivan Hurt, Dec 16 2015

Mathematica

Table[3n(6n+1), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 21, 78}, 40] (* Harvey P. Dale, Dec 17 2014 *)
CoefficientList[Series[x (21 + 15 x) / (1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 18 2014 *)

Prog

(Magma) [18*n^2+3*n: n in [0..50]]; // Vincenzo Librandi, Dec 18 2014
(PARI) a(n)=3*n*(6*n+1) \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A000217, A014105, A033585, A049453, A081266, A144312.

Sequence in context: A143206 A182754 A045559 * A010009 A172082 A296970

Adjacent sequences: A144311 A144312 A144313 * A144315 A144316 A144317

Keyword

nonn,easy

Author

Reinhard Zumkeller, Sep 17 2008

Status

approved