OFFSET
1,2
COMMENTS
Partial sums of A015577. - Mircea Merca, Dec 28 2010
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (9,1,-9).
FORMULA
a(n) = round((9*9^n-9)/80) = round((9*9^n-5)/80) = floor((9*9^n-1)/80) = ceiling((9*9-9)/80); a(n) = a(n-2) + 9^(n-1), n > 1. - Mircea Merca, Dec 28 2010
From Joerg Arndt, Jan 08 2011: (Start)
G.f.: x / ( (x-1)*(9*x-1)*(1+x) ).
a(n) = 9*a(n-1) + a(n-2) - 9*a(n-3). (End)
EXAMPLE
Base 9...........Decimal
1......................1
10.....................9
101...................82
1010.................738
10101...............6643
101010.............59787
1010101...........538084
10101010.........4842756
101010101.......43584805, etc. - Philippe Deléham, Mar 23 2014
MAPLE
seq(floor((9*9^n-1)/80), n=1..25); # Mircea Merca, Dec 28 2010
MATHEMATICA
Join[{a=1, b=9}, Table[c=8*b+9*a+1; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 06 2011 *)
Table[FromDigits[PadRight[{}, n, {1, 0}], 9], {n, 20}] (* Harvey P. Dale, May 26 2020 *)
PROG
(Magma) [Round((9*9^n-9)/80): n in [1..30]]; // Vincenzo Librandi, Jun 25 2011
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved