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COMMENTS
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Length of repeating cycle of the final n+1 digits in Fermat numbers. - Lekraj Beedassy, Robert G. Wilson v and Eric Weisstein, Jul 05 2004
Number of n-digit endings for a power of 2 whose exponent is greater than or equal to n - J. Lowell, jhbubby(AT)avana.net.
For n>=1, a(n) is equal to the number of functions f:{1,2...,n}->{1,2,3,4,5} such that for a fixed x in {1,2,...,n} and a fixed y in {1,2,3,4,5} we have f(x)<>y. - Aleksandar M. Janjic and Milan Janjic, Mar 27 2007
Contribution from Gary W. Adamson, Jul 22 2010: (Start)
Equals INVERT transform of A033887: (1, 3, 13, 55, 233,...) and INVERTi
transform of A001653: (1, 5, 29, 169, 985, 5741,...). (End)
Contribution from Gary W. Adamson, Aug 03 2010: (Start)
a(n) = (n+1) terms in the sequence (1, 3, 4, 4, 4,...) dot (n+1) terms in the
sequence (1, 1, 4, 20, 100,...). Example: a(4) = 500 = (1, 3, 4, 4, 4) dot
(1, 1, 4, 20, 100) = (1 + 3 + 16, + 80 + 400), where (1, 3, 16, 80, 400,...) =
A055842, finite differences of A005054 terms. (End)
a(n) is the number of compositions of n when there are 4 types of each natural number. [From Milan Janjic, Aug 13 2010]
Apart from the first term, number of monic squarefree polynomials over F_5 of degree n. [Charles R Greathouse IV, Feb 07 2012]
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MATHEMATICA
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f[n_]:=(4*5^n)/5; lst={}; Do[AppendTo[lst, f[n]], {n, 4!}]; lst
a=1; s=a; lst={a}; Do[AppendTo[lst, a=4*s]; s=a+s, {n, 4!}]; lst [From Vladimir Joseph Stephan Orlovsky, Nov 10 2009]
Table[EulerPhi[5^n], {n, 0, 40}] [From Vladimir Joseph Stephan Orlovsky, Nov 10 2009]
CoefficientList[Series[(1 - x) / (1 - 5 x), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 08 2013 *)
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