A165154 a(n) = 100*a(n-1) + (-9)^(n-1) for n>0, a(0)=0.

0, 1, 91, 9181, 917371, 91743661, 9174307051, 917431236541, 91743118871131, 9174311930159821, 917431192628561611, 91743119266342945501, 9174311926602913490491, 917431192660573778585581, 91743119266054835992729771, 9174311926605506476065432061

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (91,900).

Formula

From Colin Barker, Oct 02 2015: (Start)

a(n) = 91*a(n-1) + 900*a(n-2) for n>1, a(0)=0.

G.f.: x/((1+9*x)*(1-100*x)). (End)

E.g.f.: (1/109)*(exp(100*x) - exp(-9*x)). - G. C. Greubel, Feb 09 2023

Mathematica

LinearRecurrence[{91, 900}, {0, 1}, 40] (* G. C. Greubel, Feb 09 2023 *)

Prog

(Magma) [(1/109)*(100^n-(-9)^n): n in [0..20]]; // Vincenzo Librandi, Jun 10 2011
(PARI) Vec(x/((1+9*x)*(1-100*x)) + O(x^20)) \\ Colin Barker, Oct 02 2015
(SageMath) [(100^n-(-9)^n)/109 for n in range(41)] # G. C. Greubel, Feb 09 2023

Crossrefs

Cf. A021113, A164913, A165155, A172162, A172163.

Sequence in context: A054216 A109627 A095372 * A015261 A370780 A168624

Adjacent sequences: A165151 A165152 A165153 * A165155 A165156 A165157

Keyword

nonn,less,easy

Author

Mark Dols, Sep 05 2009

Extensions

a(0) prepended by Joerg Arndt, Oct 02 2015

Status

approved