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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

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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

FromWesley 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

FromAmiram Eldar, May 11 2025: (Start)

Sum_{n>=1} 1/a(n) = 2 - Pi/(2*sqrt(3)) - 2*log(2)/3 - log(3)/2.

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/3 + log(2)/3 + log(2+sqrt(3))/sqrt(3) - 2. (End)

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