OFFSET
0,2
COMMENTS
Case r=9 in a(n)=((r-2)*r^n+1)/(r-1).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-9).
FORMULA
a(n) = (7*9^n + 1)/8.
a(n) = +10*a(n-1) -9*a(n-2).
a(n) = 8*Sum_{i=0..n-1} a(i) -n + 1.
G.f.: (1-2*x)/((1-x)*(1-9*x)).
a(n) = 9^n - Sum_{i=0..n-1} 9^i for n>0. - Bruno Berselli, Jun 20 2013
E.g.f.: (7*exp(9*x) + exp(x))/8. - G. C. Greubel, Nov 06 2018
MATHEMATICA
(7*9^Range[0, 30]+1)/8 (* or *) LinearRecurrence[{10, -9}, {1, 8}, 30] (* Harvey P. Dale, Jul 20 2012 *)
PROG
(Magma) [(7*9^n+1)/8: n in [0..25]]; // Vincenzo Librandi, Mar 30 2011
(PARI) a(n)=(7*9^n+1)/8 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Sture Sjöstedt, Mar 30 2011
EXTENSIONS
Additional formulas from Bruno Berselli
STATUS
approved