A178511 a(n) = (1/119)*(100^n -(-19)^n).

1, 81, 8461, 839241, 84054421, 8402966001, 840343645981, 84033470726361, 8403364056199141, 840336082932216321, 84033614424287889901, 8403361325938530091881, 840336134807167928254261, 84033613438663809363169041, 8403361344665387622099788221

Offset: 1

Author

Mark Dols, May 29 2010

Keywords

• nonn
• frac
• easy

Comments

Numerators in alternating Sum_{n>=0} 19^n/100^(n+1).

Related to decimal expansion of fraction of 1/119 and Pell numbers. [In which way? - Joerg Arndt, May 14 2011]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..150
• Index entries for linear recurrences with constant coefficients, signature (81,1900).

Crossrefs

Cf. A000129, A021083, A038207, A178510.

Programs

Magma

[(1/119)*(100^n -(-19)^n): n in [1..20]]; // Vincenzo Librandi, May 17 2011

Mathematica

LinearRecurrence[{81,1900},{1,81},20] (* Harvey P. Dale, Nov 12 2022 *)

PARI

Vec(-x/((19*x+1)*(100*x-1)) + O(x^20)) \\ Colin Barker, Oct 02 2015

Formula

a(n+1) = a(n)*100 +- 19^n with a(0)=0 and a(1)= 1.

From Colin Barker, Oct 02 2015: (Start)

a(n) = 81*a(n-1) + 1900*a(n-2) for n > 2.

G.f.: -x / ((19*x+1)*(100*x-1)).

(End)