OFFSET
0,5
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-9,8,-4).
FORMULA
From R. J. Mathar, Mar 17 2008: (Start)
O.g.f.: x^3/((1-x+x^2)(1-2*x)^2).
a(n) = (1/3)*(2^(n-1)*(n-2) + ChebyshevU(n, 1/2)). - G. C. Greubel, Jan 05 2022
MATHEMATICA
Table[(1/3)*(2^(n-1)*(n-2) + ChebyshevU[n, 1/2]), {n, 0, 40}] (* G. C. Greubel, Jan 05 2022 *)
LinearRecurrence[{5, -9, 8, -4}, {0, 0, 0, 1}, 40] (* Harvey P. Dale, Apr 30 2023 *)
PROG
(Magma) [n le 4 select Floor((n-1)/3) else 5*Self(n-1) -9*Self(n-2) +8*Self(n-3) -4*Self(n-4): n in [1..30]]; // G. C. Greubel, Jan 05 2022
(Sage) [(1/3)*(2^(n-1)*(n-2) + chebyshev_U(n, 1/2)) for n in (0..40)] # G. C. Greubel, Jan 05 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul Curtz, Mar 07 2008
EXTENSIONS
More terms from R. J. Mathar, Mar 17 2008
STATUS
approved