OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Pieter Moree, The formal series Witt transform, Discr. Math. no. 295 vol. 1-3 (2005) 143-160.
Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).
FORMULA
G.f.: 2*x*(1+x)*(1+x^2)/((1-x)^3*(1+x+x^2)).
a(n) = 2*A071619(n).
From G. C. Greubel, Oct 24 2022: (Start)
a(n) = 4*(2 - 2*n + n^2) - a(n-1) - a(n-2).
MATHEMATICA
CoefficientList[Series[2x(1+x)(1 +x^2)/((1-x)^3 (1+x+x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 14 2012 *)
LinearRecurrence[{2, -1, 1, -2, 1}, {0, 2, 6, 12, 22}, 50] (* Harvey P. Dale, Jul 04 2021 *)
PROG
(Magma) [n le 2 select 1+(-1)^n else 4*(1+(n-2)^2) - Self(n-1) - Self(n-2): n in [1..30]]; // G. C. Greubel, Oct 24 2022
(SageMath) [2*(2*(1+3*n^2) -(2*chebyshev_U(n, -1/2) +chebyshev_U(n-1, -1/2)))/9 for n in range(41)] # G. C. Greubel, Oct 24 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Nov 08 2008
STATUS
approved