A038867 a(n) = (n+5)^3 - n^3.

125, 215, 335, 485, 665, 875, 1115, 1385, 1685, 2015, 2375, 2765, 3185, 3635, 4115, 4625, 5165, 5735, 6335, 6965, 7625, 8315, 9035, 9785, 10565, 11375, 12215, 13085, 13985, 14915, 15875, 16865, 17885, 18935, 20015, 21125, 22265, 23435, 24635, 25865, 27125

Offset

0,1

Comments

From Klaus Purath, May 15 2026: (Start)

With a(-1) = 65, a(-2) = 35, numbers k such that 60*k - 1875 is a perfect square.

Conjecture: There are no squares in this sequence, verified up to n = 100000. (End)

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.: 5*(25-32*x+13*x^2)/(1-x)^3. - R. J. Mathar, Apr 03 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jul 07 2012

From Elmo R. Oliveira, Sep 12 2025: (Start)

E.g.f.: 5*exp(x)*(25 + 18*x + 3*x^2).

a(n) = 5*(3*n^2 + 15*n + 25).

a(n) = 5*A378569(n+2). (End)

Mathematica

CoefficientList[Series[5*(25-32*x+13*x^2)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 07 2012 *)
(* Alternative: *)
LinearRecurrence[{3, -3, 1}, {125, 215, 335}, 40] (* Harvey P. Dale, Mar 30 2018 *)

Prog

(Magma) [((n+5)^3 - n^3): n in [0..50]]; // Vincenzo Librandi, Jul 07 2012
(PARI) a(n)=(n+5)^3-n^3 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A378569.

Sequence in context: A251125 A252065 A252058 * A378355 A029782 A390188

Adjacent sequences: A038864 A038865 A038866 * A038868 A038869 A038870

Keyword

nonn,easy

Author

Jeff Burch

Extensions

G.f.: adapted to the offset 0 and added 125 by Vincenzo Librandi, Jul 07 2012

Status

approved