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

0, 4, 24, 124, 624, 3124, 15624, 78124, 390624, 1953124, 9765624, 48828124, 244140624, 1220703124, 6103515624, 30517578124, 152587890624, 762939453124, 3814697265624, 19073486328124, 95367431640624

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

Examples

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

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).

Crossrefs

Cf. A000351, A003463, A125831, A248722.

Programs

Magma

[5^n-1: n in [0..30]]; // Vincenzo Librandi, Jun 06 2011

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 *)

PARI

a(n)=5^n-1 \\ Charles R Greathouse IV, Apr 17 2012

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

a(n) = 2*A125831(n) = 4*A003463(n). - Elmo R. Oliveira, Dec 10 2023