A028494 a(n) = -(1/2)*(n+2)*(n^2 - 6*n - 1).

1, 9, 18, 25, 27, 21, 4, -27, -75, -143, -234, -351, -497, -675, -888, -1139, -1431, -1767, -2150, -2583, -3069, -3611, -4212, -4875, -5603, -6399, -7266, -8207, -9225, -10323, -11504, -12771, -14127, -15575, -17118, -18759, -20501, -22347, -24300, -26363

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..740

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

Formula

From Elmo R. Oliveira, Sep 08 2025: (Start)

G.f.: (3*x^3 - 12*x^2 + 5*x + 1)/(-1+x)^4.

E.g.f.: (-x^3 + x^2 + 16*x + 2)*exp(x)/2.

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

Mathematica

Table[-(1/2)(n+2)(n^2-6n-1), {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 9, 18, 25}, 40] (* Harvey P. Dale, Sep 08 2018 *)

Prog

(Magma) [-1/2*(n+2)*(n^2-6*n-1): n in [0..40]]; // Vincenzo Librandi, Apr 27 2011
(PARI) a(n)=-(n+2)*(n^2-6*n-1)/2 \\ Charles R Greathouse IV, Oct 18 2022

Crossrefs

Sequence in context: A232056 A109661 A015798 * A167663 A390365 A347242

Adjacent sequences: A028491 A028492 A028493 * A028495 A028496 A028497

Keyword

sign,easy

Author

N. J. A. Sloane

Status

approved