A015238 a(n) = (2*n - 3)n^2.

0, -1, 4, 27, 80, 175, 324, 539, 832, 1215, 1700, 2299, 3024, 3887, 4900, 6075, 7424, 8959, 10692, 12635, 14800, 17199, 19844, 22747, 25920, 29375, 33124, 37179, 41552, 46255, 51300, 56699, 62464, 68607, 75140, 82075, 89424, 97199, 105412, 114075, 123200, 132799

Offset

0,3

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

G.f.: x*(-1 + 8*x + 5*x^2)/(1-x)^4. - Ivan Panchenko, Nov 09 2013

From G. C. Greubel, Jul 30 2016: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

E.g.f.: (-x + 3*x^2 + 2*x^3)*exp(x). (End)

From Amiram Eldar, Jul 10 2026: (Start)

Sum_{n>=1} 1/a(n) = 4*(log(2)-1)/9 - Pi^2/18.

Sum_{n>=1} (-1)^n/a(n) = (Pi^2 + 4*Pi + 8*log(2) + 16)/36. (End)

Mathematica

Table[(2 n^3 - 3 n^2), {n, 0, 40}] (* Vincenzo Librandi, Aug 03 2014 *)
(* Alternative: *)
LinearRecurrence[{4, -6, 4, -1}, {0, -1, 4, 27}, 40] (* Harvey P. Dale, Oct 11 2025 *)

Prog

(Magma) [2*n^3-3*n^2: n in [0..40]]; // Vincenzo Librandi, Aug 03 2014
(PARI) a(n)=(2*n-3)*n^2 \\ Charles R Greathouse IV, Jul 30 2016

Crossrefs

Sequence in context: A071837 A334633 A266011 * A298987 A070600 A357841

Adjacent sequences: A015235 A015236 A015237 * A015239 A015240 A015241

Keyword

sign,easy

Author

N. J. A. Sloane, Dec 11 1999

Status

approved