OFFSET
0,2
COMMENTS
Partial sums of 81^n.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..530
Index entries for linear recurrences with constant coefficients, signature (82, -81).
FORMULA
G.f.: 1/((1-x)*(1-81*x)).
a(n) = 82*a(n-1) - 81*a(n-2) for n > 1, a(0)=1, a(1)=82.
a(n) = 81*a(n-1) + 1 for n > 0, a(0)=1.
a(n) = A033119(2*n+1).
a(n) = ( 81^(n+1) - 1 ) / 80. [Bruno Berselli, Mar 24 2014]
EXAMPLE
Base 9................Decimal
1...........................1
101........................82
10101....................6643
1010101................538084
101010101............43584805
10101010101........3530369206
1010101010101....285959905687, etc.
MATHEMATICA
CoefficientList[Series[1/((1 - x) (1 - 81 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 24 2014 *)
PROG
(Magma) [(81^(n+1)-1)/80: n in [0..20]]; // Vincenzo Librandi, Mar 24 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Mar 23 2014
STATUS
approved