OFFSET
0,2
COMMENTS
Double binomial transform of [1, 3, -5, 13, -31, 75, -181, ...] = the Pell-like sequence A048655: (1, 5, 11, 27, 65, 157, ...). - Gary W. Adamson, Jul 23 2008
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,1).
FORMULA
From R. J. Mathar, Feb 23 2008: (Start)
O.g.f.: (-1 + 5*x)/(1 - 2*x - x^2).
a(n) = ((3+sqrt(2))*(1+sqrt(2))^n + (3-sqrt(2))*(1-sqrt(2))^n)/2 with offset 0. - Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009
MATHEMATICA
LinearRecurrence[{2, 1}, {-1, 3}, 25] (* G. C. Greubel, Oct 17 2016 *)
PROG
(PARI) a(n)=([0, 1; 1, 2]^n*[-1; 3])[1, 1] \\ Charles R Greathouse IV, Oct 17 2016
(Magma) I:=[-1, 3]; [n le 2 select I[n] else 2*Self(n-1) + Self(n-2): n in [1..30]]; // G. C. Greubel, May 22 2021
(Sage) [(lucas_number2(n, 2, -1) + 2*lucas_number2(n-1, 2, -1))/2 for n in (0..30)] # G. C. Greubel, May 22 2021
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Feb 21 2008
EXTENSIONS
More terms from R. J. Mathar, Feb 23 2008
STATUS
approved