A239670 Expansion of 1/((1-x)*(1-81*x)).

1, 82, 6643, 538084, 43584805, 3530369206, 285959905687, 23162752360648, 1876182941212489, 151970818238211610, 12309636277295140411, 997080538460906373292, 80763523615333416236653, 6541845412842006715168894, 529889478440202543928680415

Offset: 0

Author

Philippe Deléham, Mar 23 2014

Keywords

• nonn
• easy

Comments

Partial sums of 81^n.

Examples

			Base 9................Decimal
1...........................1
101........................82
10101....................6643
1010101................538084
101010101............43584805
10101010101........3530369206
1010101010101....285959905687, etc.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..530
• Index entries for linear recurrences with constant coefficients, signature (82, -81).

Crossrefs

Cf. A033119.

Programs

Magma

[(81^(n+1)-1)/80: n in [0..20]]; // Vincenzo Librandi, Mar 24 2014

Mathematica

CoefficientList[Series[1/((1 - x) (1 - 81 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 24 2014 *)

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]