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 (6, -9, 4).
FORMULA
a(0)=1; a(n+1) = 4*a(n) - n.
a(n) = (5*4^n + 3*n + 4)/9.
From R. J. Mathar, Aug 09 2009: (Start)
a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3).
G.f.: (1-3*x+x^2)/((1-4*x)*(1-x)^2). (End)
E.g.f.: (1/9)*(5*exp(4*x) + (3*x + 4)*exp(x)). - G. C. Greubel, Sep 08 2017
MATHEMATICA
Table[(5*4^n + 3*n + 4)/9, {n, 0, 50}] (* G. C. Greubel, Sep 08 2017 *)
PROG
(PARI) x='x+O('x^50); Vec((1-3*x+x^2)/((1-4*x)*(1-x)^2)) \\ G. C. Greubel, Sep 08 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Rolf Pleisch, Aug 08 2009
STATUS
approved