OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: (1-x-x^2)/(1-4*x-4*x^2) . a(n)=3*A086347(n), n>=1 .
From G. C. Greubel, Mar 25 2021: (Start)
a(n) = (1/4)*[n=0] - 3*(2*i)^(n-2)*ChebyshevU(n, -i).
a(n) = (1/4)*[n=0] + 3*2^(n-2)*P_{n+1}, where P_{n} = A000129(n) (Pell numbers). (End)
MAPLE
1, seq(simplify(-3*(2*I)^(n-2)*ChebyshevU(n, -I)), n = 1..30); # G. C. Greubel, Mar 25 2021
MATHEMATICA
With[{m=4}, LinearRecurrence[{m, m}, {1, m-1, m^2-1}, 30]] (* G. C. Greubel, Mar 25 2021 *)
PROG
(Magma) m:=4; [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=4; [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
AUTHOR
Philippe Deléham, Jan 20 2009
STATUS
approved