OFFSET
0,2
COMMENTS
Numbers whose base 5 representation is 44444.......4. - Zerinvary Lajos, Feb 03 2007
For n > 0, a(n) is the sum of divisors of 3*5^(n-1). - Patrick J. McNab, May 27 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
Amelia Carolina Sparavigna, The groupoids of Mersenne, Fermat, Cullen, Woodall and other Numbers and their representations by means of integer sequences, Politecnico di Torino, Italy (2019), [math.NT].
Amelia Carolina Sparavigna, Some Groupoids and their Representations by Means of Integer Sequences, International Journal of Sciences (2019) Vol. 8, No. 10.
Index entries for linear recurrences with constant coefficients, signature (6,-5).
FORMULA
G.f.: 1/(1-5*x) - 1/(1-x) = 4*x/((1-5*x)*(1-x)). - Mohammad K. Azarian, Jan 14 2009
E.g.f.: exp(5*x) - exp(x). - Mohammad K. Azarian, Jan 14 2009
a(n+1) = 5*a(n) + 4. - Reinhard Zumkeller, Nov 22 2009
a(n) = Sum_{i=1..n} 4^i*binomial(n,n-i) for n>0, a(0)=0. - Bruno Berselli, Nov 11 2015
a(n) = A000351(n) - 1. - Sean A. Irvine, Jun 19 2019
Sum_{n>=1} 1/a(n) = A248722. - Amiram Eldar, Nov 13 2020
EXAMPLE
For n = 5, a(5) = 4*5 + 16*10 + 64*10 + 256*5 + 1024*1 = 3124. - Bruno Berselli, Nov 11 2015
MATHEMATICA
5^Range[0, 50]-1 (* Vladimir Joseph Stephan Orlovsky, Feb 20 2011 *)
LinearRecurrence[{6, -5}, {0, 4}, 30] (* Harvey P. Dale, Apr 06 2019 *)
PROG
(Magma) [5^n-1: n in [0..30]]; // Vincenzo Librandi, Jun 06 2011
(PARI) a(n)=5^n-1 \\ Charles R Greathouse IV, Apr 17 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved