A127975 Repeat 3^n three times.
1, 1, 1, 3, 3, 3, 9, 9, 9, 27, 27, 27, 81, 81, 81, 243, 243, 243, 729, 729, 729, 2187, 2187, 2187, 6561, 6561, 6561, 19683, 19683, 19683, 59049, 59049, 59049, 177147, 177147, 177147, 531441, 531441, 531441, 1594323, 1594323, 1594323, 4782969, 4782969, 4782969
Offset: 0
Examples
a(6)=9 since there are exactly 9 functions f:[7]->[3], denoted by <f(1),f(2),...,f(7)>, with f(1)=1 and with f(x)=f(y) whenever y=ceiling(x/3). The nine functions are <1,1,1,1,1,1,1>, <1,1,1,1,1,1,2>, <1,1,1,1,1,1,3>, <1,1,1,2,2,2,1>, <1,1,1,2,2,2,2>, <1,1,1,2,2,2,3>, <1,1,1,3,3,3,1>, <1,1,1,3,3,3,2>, and <1,1,1,3,3,3,3>. - _Dennis P. Walsh_, Sep 06 2018
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..6000
- Index entries for linear recurrences with constant coefficients, signature (0,0,3).
Programs
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Magma
[3^(Floor(n/3)):n in [0..50]]; // Vincenzo Librandi, Sep 20 2011
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Maple
seq(3^floor(n/3),n=0..45); # Dennis P. Walsh, Sep 06 2018
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Mathematica
CoefficientList[Series[(1+x+x^2)/(1-3*x^3), {x,0,50}], x] (* or *) Table[3^(Floor[n/3]), {n,0,50}] (* G. C. Greubel, Apr 30 2017 *) -
PARI
a(n)=3^(n\3) \\ Charles R Greathouse IV, Oct 03 2016
Formula
G.f.: (1+x+x^2)/(1-3*x^3).
Extensions
Edited and corrected by R. J. Mathar, Jun 14 2008
Comments