OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,5).
FORMULA
G.f.: (1 - x - x^2) / (1 - 5*x - 5*x^2).
a(n) = (1/5)*[n=0] - 4*(sqrt(5)*i)^(n-2)*ChebyshevU(n, -sqrt(5)*i/2). - G. C. Greubel, Mar 25 2021
E.g.f.: (3 + 4*exp(5*x/2)*(3*cosh(3*sqrt(5)*x/2) + sqrt(5)*sinh(3*sqrt(5)*x/2)))/15. - Stefano Spezia, May 31 2023
MATHEMATICA
With[{m=5}, LinearRecurrence[{m, m}, {1, m-1, m^2-1}, 30]] (* G. C. Greubel, Mar 25 2021 *)
PROG
(Magma) m:=5; [1] cat [n le 2 select (m-1)*(m*n-(m-1)) else m*(Self(n-1) + Self(n-2)): n in [1..30]]; // G. C. Greubel, Mar 25 2021
(Sage) m=5; [1]+[-(m-1)*(sqrt(m)*i)^(n-2)*chebyshev_U(n, -sqrt(m)*i/2) for n in (1..30)] # G. C. Greubel, Mar 25 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Jan 20 2009
EXTENSIONS
a(20) corrected and a(21) from Sean A. Irvine, May 19 2019
STATUS
approved