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A024049 a(n) = 5^n - 1. 28

%I

%S 0,4,24,124,624,3124,15624,78124,390624,1953124,9765624,48828124,

%T 244140624,1220703124,6103515624,30517578124,152587890624,

%U 762939453124,3814697265624,19073486328124,95367431640624

%N a(n) = 5^n - 1.

%C Numbers n for which the expression 5^n/(n+1) is an integer. - _Paolo P. Lava_, May 29 2006

%C Numbers whose base 5 representation is 44444.......4. - _Zerinvary Lajos_, Feb 03 2007

%C For n > 0, a(n) is the sum of divisors of 3 * 5^(n-1). - _Patrick J. McNab_, May 27 2017

%H Vincenzo Librandi, <a href="/A024049/b024049.txt">Table of n, a(n) for n = 0..400</a>

%H Amelia Carolina Sparavigna, <a href="https://doi.org/10.5281/zenodo.3471358">The groupoids of Mersenne, Fermat, Cullen, Woodall and other Numbers and their representations by means of integer sequences</a>, Politecnico di Torino, Italy (2019), [math.NT].

%H Amelia Carolina Sparavigna, <a href="https://doi.org/10.18483/ijSci.2188">Some Groupoids and their Representations by Means of Integer Sequences</a>, International Journal of Sciences (2019) Vol. 8, No. 10.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-5).

%F G.f.: 1/(1-5*x)-1/(1-x). [_Mohammad K. Azarian_, Jan 14 2009]

%F E.g.f.: e^(5*x)-e^x. [_Mohammad K. Azarian_, Jan 14 2009]

%F a(n+1) = 5*a(n) + 4. [_Reinhard Zumkeller_, Nov 22 2009]

%F a(n) = Sum_{i=1..n} 4^i*binomial(n,n-i) for n>0, a(0)=0. [_Bruno Berselli_, Nov 11 2015]

%F a(n) = A000351(n) - 1. - _Sean A. Irvine_, Jun 19 2019

%e For n=5, a(5) = 4*5 + 16*10 + 64*10 + 256*5 + 1024*1 = 3124. [_Bruno Berselli_, Nov 11 2015]

%t 5^Range[0,50]-1 (* _Vladimir Joseph Stephan Orlovsky_, Feb 20 2011 *)

%t LinearRecurrence[{6,-5},{0,4},30] (* _Harvey P. Dale_, Apr 06 2019 *)

%o (MAGMA) [5^n-1: n in [0..30]]; // _Vincenzo Librandi_, Jun 06 2011

%o (PARI) a(n)=5^n-1 \\ _Charles R Greathouse IV_, Apr 17 2012

%Y Cf. A000351.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified April 7 13:01 EDT 2020. Contains 333305 sequences. (Running on oeis4.)