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

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). [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]

a(n) = A000351(n) - 1. - Sean A. Irvine, Jun 19 2019

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

Cf. A000351.

Sequence in context: A049315 A295506 A098224 * A103455 A289715 A174443

Adjacent sequences:  A024046 A024047 A024048 * A024050 A024051 A024052

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 17 23:35 EST 2020. Contains 332006 sequences. (Running on oeis4.)