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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..100
- Index entries for linear recurrences with constant coefficients, signature (91,900).
Programs
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Magma
[(1/109)*(100^n-(-9)^n): n in [0..20]]; // Vincenzo Librandi, Jun 10 2011
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Mathematica
LinearRecurrence[{91,900}, {0,1}, 40] (* G. C. Greubel, Feb 09 2023 *) -
PARI
Vec(x/((1+9*x)*(1-100*x)) + O(x^20)) \\ Colin Barker, Oct 02 2015
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SageMath
[(100^n-(-9)^n)/109 for n in range(41)] # G. C. Greubel, Feb 09 2023
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
Extensions
a(0) prepended by Joerg Arndt, Oct 02 2015