OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-3).
FORMULA
a(n) = 3*a(n-1) + 10 with a(0)=-4.
G.f.: 2*(7*x - 2)/((1-x)*(1-3*x)). - Vincenzo Librandi, Jul 06 2012
a(n) = 4*a(n-1) - 3*a(n-2). - Vincenzo Librandi, Jul 06 2012
E.g.f.: exp(3*x) - 5*exp(x). - G. C. Greubel, Jul 27 2016
MATHEMATICA
CoefficientList[Series[2*(7*x-2)/((1-x)*(1-3*x)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 06 2012 *)
LinearRecurrence[{4, -3}, {-4, -2}, 25] (* G. C. Greubel, Jul 27 2016 *)
3^Range[0, 30]-5 (* Harvey P. Dale, Sep 12 2022 *)
PROG
(Magma) I:=[-4, -2]; [n le 2 select I[n] else 4*Self(n-1)-3*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jul 06 2012
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Vincenzo Librandi, Dec 01 2009
EXTENSIONS
Formula and examples edited to use correct offset by Jon E. Schoenfield, Jun 19 2010
STATUS
approved