A153259 a(n) = n^3 - (3*(n+3))^2.

-81, -143, -217, -297, -377, -451, -513, -557, -577, -567, -521, -433, -297, -107, 143, 459, 847, 1313, 1863, 2503, 3239, 4077, 5023, 6083, 7263, 8569, 10007, 11583, 13303, 15173, 17199, 19387, 21743, 24273, 26983, 29879, 32967, 36253, 39743, 43443, 47359

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), a(1)=-81, a(2)=-143, a(3)=-217, a(4)=-297. - Harvey P. Dale, Jul 10 2013

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

G.f.: x*(-81 + 181*x - 131*x^2 + 37*x^3)/(x-1)^4.

E.g.f.: exp(x)*(-81 - 62*x - 6*x^2 + x^3). (End)

Mathematica

a[n_]:=n^3-(3*(n+3))^2; lst={}; Do[AppendTo[lst, a[n]], {n, 0, 5!}]; lst
Table[n^3-(3(n+3))^2, {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {-81, -143, -217, -297}, 40] (* Harvey P. Dale, Jul 10 2013 *)

Prog

(PARI) a(n)=n^3-(3*n+9)^2 \\ Charles R Greathouse IV, Oct 18 2022

Crossrefs

Cf. A045991, A069778, A081437, A153257, A153258.

Sequence in context: A371846 A046317 A046374 * A369977 A207050 A206072

Adjacent sequences: A153256 A153257 A153258 * A153260 A153261 A153262

Keyword

sign,easy

Author

Vladimir Joseph Stephan Orlovsky, Dec 22 2008

Status

approved