OFFSET
0,2
COMMENTS
Binomial transform of A082541.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-4).
FORMULA
a(n) = (7*4^n-4)/3.
G.f.: (1+3*x)/((1-4*x)*(1-x)).
E.g.f.: (7*exp(4*x)-4*exp(x))/3.
a(n) = 4*a(n-1) + 4, n > 0. - Gary Detlefs, Jun 23 2010
a(0)=1, a(1)=8, a(n) = 5*a(n-1) - 4*a(n-2). - Harvey P. Dale, Jul 23 2011
MATHEMATICA
(7*4^Range[0, 25]-4)/3 (* or *) LinearRecurrence[{5, -4}, {1, 8}, 26] (* Harvey P. Dale, Jul 23 2011 *)
CoefficientList[Series[(1 + 3 x)/((1 - 4 x) (1 - x)), {x, 0, 22}], x] (* Michael De Vlieger, Mar 03 2017 *)
PROG
(Magma) [(7*4^n-4)/3: n in [0..25]]; // Vincenzo Librandi, Jul 24 2011
(PARI) a(n)=(7*4^n-4)/3 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 02 2003
STATUS
approved