A081552 Leading terms of rows in A081551.
1, 11, 102, 1003, 10004, 100005, 1000006, 10000007, 100000008, 1000000009, 10000000010, 100000000011, 1000000000012, 10000000000013, 100000000000014, 1000000000000015, 10000000000000016, 100000000000000017, 1000000000000000018
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..300
- Index entries for linear recurrences with constant coefficients, signature (12,-21,10).
Programs
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Magma
[10^(n-1)+n-1: n in [1..20]]; // Vincenzo Librandi, Jun 16 2013
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Magma
I:=[1, 11, 102]; [n le 3 select I[n] else 12*Self(n-1)-21*Self(n-2)+10*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 16 2013
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Maple
seq(10^(n-1) +n-1, n=1..40); # G. C. Greubel, May 27 2021
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Mathematica
Table[10^(n-1) +n-1, {n,30}] (* or *) CoefficientList[Series[(1-x-9x^2)/((1-10x)(1-x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 16 2013 *) -
Sage
[10^(n-1) +n-1 for n in (1..40)] # G. C. Greubel, May 27 2021
Formula
a(n) = 10^(n-1) + n-1.
G.f.: x*(1 -x -9*x^2)/((1-10*x)*(1-x)^2). - Vincenzo Librandi, Jun 16 2013
a(n) = 12*a(n-1) -21*a(n-2) +10*a(n-3). - Vincenzo Librandi, Jun 16 2013
E.g.f.: (1/10)*(9 - 10*(1-x)*exp(x) + exp(10*x)). - G. C. Greubel, May 27 2021
Comments