OFFSET
0,2
COMMENTS
Binomial transform of 1,1,4,1,4,1,4,1,4,1,4,1,4,1,4,... - _Philippe Deleham_, Jan 05 2009
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
From Philippe Deléham, Jan 05 2009: (Start)
a(n) = 3*a(n-1) - 2*a(n-2), n > 2.
a(n) = 2*a(n-1) + 3, n > 1.
a(n) = 5*2^(n-1) - 3, n >= 1. (End)
E.g.f.: (1/2)*(3 - 6*exp(x) + 5*exp(2*x)). - G. C. Greubel, Sep 02 2016
MATHEMATICA
Join[{1}, Table[ 5*2^(n - 1) - 3, {n, 1, 10}]] (* or *) Join[{1, 2, 7}, LinearRecurrence[{3, -2}, {17, 37}, 10]] (* G. C. Greubel, Sep 02 2016 *)
PROG
(Magma) [1] cat [5*2^n-3 : n in [0..30]]; // Vincenzo Librandi, Nov 11 2011
(PARI) a(n)=if(n, 5<<(n-1)-3, 1) \\ Charles R Greathouse IV, Sep 02 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Dec 15 2008
EXTENSIONS
a(0) added by Philippe Deléham, Jan 05 2009
STATUS
approved