A003953 Expansion of g.f.: (1+x)/(1-10*x).
1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 110000000000, 1100000000000, 11000000000000, 110000000000000, 1100000000000000, 11000000000000000
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 312
- Index to divisibility sequences
- Index entries for linear recurrences with constant coefficients, signature (10).
- Index entries for sequences related to trees
Programs
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GAP
k:=11;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019
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Magma
k:=11; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 24 2019
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Maple
k:=11; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # modified by G. C. Greubel, Sep 24 2019
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Mathematica
Join[{1}, 11*10^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *) Join[{1},NestList[10#&,11,20]] (* Harvey P. Dale, Jul 04 2025 *) -
PARI
a(n)=11*10^n\10 \\ Charles R Greathouse IV, Aug 14 2015
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Sage
k=11; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 24 2019
Formula
a(n) = Sum_{k=0..n} A029653(n, k)*x^k for x = 9. - Philippe Deléham, Jul 10 2005
G.f.: (1+x)/(1-10*x). - Paul Barry, Mar 22 2006
a(0) = 1, a(n) = 10^n + 10^(n-1) = 11*10^(n-1) for n >= 1. - Jaroslav Krizek, Aug 17 2009
E.g.f.: (11*exp(10*x) - 1)/10. - G. C. Greubel, Sep 24 2019
Extensions
Edited by N. J. A. Sloane, Dec 04 2009
Comments