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%I #68 Feb 18 2024 02:03:01
%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 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) = 4*x/((1-5*x)*(1-x)). - _Mohammad K. Azarian_, Jan 14 2009
%F E.g.f.: exp(5*x) - exp(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
%F Sum_{n>=1} 1/a(n) = A248722. - _Amiram Eldar_, Nov 13 2020
%F a(n) = 2*A125831(n) = 4*A003463(n). - _Elmo R. Oliveira_, Dec 10 2023
%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, A003463, A125831, A248722.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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