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A024049 a(n) = 5^n-1. 27
0, 4, 24, 124, 624, 3124, 15624, 78124, 390624, 1953124, 9765624, 48828124, 244140624, 1220703124, 6103515624, 30517578124, 152587890624, 762939453124, 3814697265624, 19073486328124, 95367431640624 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Numbers n for which the expression 5^n/(n+1) is an integer. - Paolo P. Lava, May 29 2006

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

Index entries for linear recurrences with constant coefficients, signature (6,-5).

FORMULA

G.f.: 1/(1-5*x)-1/(1-x). [Mohammad K. Azarian, Jan 14 2009]

E.g.f.: e^(5*x)-e^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]

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*)

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

Sequence in context: A273444 A049315 A098224 * A103455 A174443 A180222

Adjacent sequences:  A024046 A024047 A024048 * A024050 A024051 A024052

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified July 25 04:48 EDT 2017. Contains 289779 sequences.