A133472 a(n) = 10^n + 5.
6, 15, 105, 1005, 10005, 100005, 1000005, 10000005, 100000005, 1000000005, 10000000005, 100000000005, 1000000000005, 10000000000005, 100000000000005, 1000000000000005, 10000000000000005, 100000000000000005, 1000000000000000005, 10000000000000000005, 100000000000000000005
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..500
- Index entries for linear recurrences with constant coefficients, signature (11,-10).
Programs
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Magma
[10^n+5: n in [0..20]]; // Vincenzo Librandi, Aug 10 2011
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Mathematica
Join[{6},Table[10*FromDigits[PadRight[{1},n,0]]+5,{n,20}]] (* or *) LinearRecurrence[{11,-10},{6,15},20] (* Harvey P. Dale, Sep 06 2020 *) -
PARI
apply( {A133472(n)=10^n+5}, [0..20]) \\ M. F. Hasler, Jun 15 2025
Formula
From R. J. Mathar, Nov 30 2007: (Start)
O.g.f.: -3*(-2+17*x)/((-1+x)*(-1+10*x)) = -5/(-1+x) - 1/(-1+10*x).
a(n) = 10*a(n-1) - 45. (End)
a(n) = 10^n + 5. - Vincenzo Librandi, Aug 10 2011
From Elmo R. Oliveira, Jun 09 2025: (Start)
E.g.f.: exp(x)*(5 + exp(9*x)).
a(n) = 11*a(n-1) - 10*a(n-2).
a(n) = 3*A133473(n). (End)
Extensions
Renamed by editors, Jun 16 2025