A213223 a(n) = 10^n + 10*n.
1, 20, 120, 1030, 10040, 100050, 1000060, 10000070, 100000080, 1000000090, 10000000100, 100000000110, 1000000000120, 10000000000130, 100000000000140, 1000000000000150, 10000000000000160, 100000000000000170, 1000000000000000180, 10000000000000000190, 100000000000000000200
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (12,-21,10).
Crossrefs
Cf. A198400.
Programs
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Magma
[10^n + 10*n: n in [0..25]];
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Magma
I:=[1, 20, 120]; [n le 3 select I[n] else 12*Self(n-1)-21*Self(n-2)+10*Self(n-3): n in [1..30]];
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Mathematica
Table[(10^n + 10 n), {n, 0, 30}] (* or *) CoefficientList[Series[(1 + 8 x - 99 x^2)/((1 - x)^2 (1 - 10 x)), {x, 0, 30}], x]
Formula
G.f.: (1+8*x-99*x^2)/((1-x)^2*(1-10*x)).
a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3) for n > 2.
E.g.f.: exp(x)*(exp(9*x) + 10*x). - Elmo R. Oliveira, Aug 29 2024