OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
From Vincenzo Librandi, May 29 2014: (Start)
G.f.: 4*x*(1 + 10*x + x^2)/(1 - x)^4.
a(n) = 4*n*(2*n^2 - 1). (End)
From Elmo R. Oliveira, Jul 06 2026: (Start)
a(n) = 4*A007588(n).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
E.g.f.: 4*x*exp(x)*(1 + 6*x + 2*x^2). (End)
MATHEMATICA
Table[ChebyshevU[3, n], {n, 0, 100}]
(* Alternative: *)
Table[4n*(2*n^2-1), {n, 0, 100}]
(* Alternative: *)
CoefficientList[Series[4 x (1 + 10 x + x^2)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, May 29 2014 *)
(* Alternative: *)
LinearRecurrence[{4, -6, 4, -1}, {0, 4, 56, 204}, 40] (* Harvey P. Dale, Dec 23 2022 *)
PROG
(Magma) [8*n^3-4*n: n in [0..40]]; // Vincenzo Librandi, May 29 2014
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Vladimir Joseph Stephan Orlovsky, Sep 11 2008
STATUS
approved
