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

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Comments

Partial sums of A015577. - Mircea Merca, Dec 28 2010

Examples

			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
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (9,1,-9).

Crossrefs

Cf. A015577.

Programs

Magma

[Round((9*9^n-9)/80): n in [1..30]]; // Vincenzo Librandi, Jun 25 2011

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 *)

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)