A276352 a(n) = 100^n - 10^n.
0, 90, 9900, 999000, 99990000, 9999900000, 999999000000, 99999990000000, 9999999900000000, 999999999000000000, 99999999990000000000, 9999999999900000000000, 999999999999000000000000, 99999999999990000000000000, 9999999999999900000000000000, 999999999999999000000000000000
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (110,-1000).
Programs
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Magma
[100^n-10^n : n in [0..20]]; // Wesley Ivan Hurt, Sep 07 2016
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Maple
A276352:=n->100^n-10^n: seq(A276352(n), n=0..20); # Wesley Ivan Hurt, Sep 07 2016
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Mathematica
Table[100^n - 10^n, {n, 0, 10}] (* Alonso del Arte, Aug 31 2016 *) -
PARI
a(n)=100^n-10^n \\ Charles R Greathouse IV, Sep 01 2016
Formula
a(n) = floor((1000^n)/(10^n + 1)).
a(n) = 9*A138147(n), for n>0.
a(n) = A168624(n) - 1.
a(n) = Sum_{k=1..n} 9*10^(2n-k).
a(n) = ((10^n)*A002283(2n))/(10^n + 1).
From Chai Wah Wu, Sep 01 2016: (Start)
a(n) = 110*a(n-1) - 1000*a(n-2) for n > 1.
G.f.: 90*x/((10*x - 1)*(100*x - 1)). (End)
E.g.f.: exp(10*x)*(exp(90*x) - 1). - Elmo R. Oliveira, Aug 14 2024