A033119 Base-9 digits are, in order, the first n terms of the periodic sequence with initial period 1,0.

1, 9, 82, 738, 6643, 59787, 538084, 4842756, 43584805, 392263245, 3530369206, 31773322854, 285959905687, 2573639151183, 23162752360648, 208464771245832, 1876182941212489, 16885646470912401, 151970818238211610

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

Cf. A015577.

Sequence in context: A293803 A263817 A288789 * A033127 A361715 A099371

Adjacent sequences: A033116 A033117 A033118 * A033120 A033121 A033122

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved