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 (2,5).
FORMULA
a(n) = ((3+2*sqrt(6))*(1+sqrt(6))^n + (3-2*sqrt(6))*(1-sqrt(6))^n)/6. - Klaus Brockhaus, Aug 15 2009
From Klaus Brockhaus, Aug 15 2009: (Start)
G.f.: (1+3*x)/(1-2*x-5*x^2).
Binomial transform of A164532.
Inverse binomial transform of A164549. (End)
a(n) = (sqrt(5)*i)^(n-1)*(sqrt(5)*i*ChebyshevU(n, -i/sqrt(5)) + 3*ChebyshevU(n-1, -i/sqrt(5))) for n > 0 with a(0) = 1. - G. C. Greubel, Jul 13 2021
MATHEMATICA
LinearRecurrence[{2, 5}, {1, 5}, 31] (* G. C. Greubel, Jul 13 2021 *)
PROG
(Magma) [ n le 2 select 4*n-3 else 2*Self(n-1)+5*Self(n-2): n in [1..24] ]; // Klaus Brockhaus, Aug 15 2009
(Sage) [1]+[(sqrt(5)*i)^(n-1)*(sqrt(5)*i*chebyshev_U(n, -i/sqrt(5)) + 3*chebyshev_U(n-1, -i/sqrt(5))) for n in (1..30)] # G. C. Greubel, Jul 13 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Sep 23 2006
EXTENSIONS
Edited by N. J. A. Sloane, Aug 27 2009, using simpler definition suggested by Klaus Brockhaus, Aug 15 2009
STATUS
approved