A024062 a(n) = 6^n - 1.

0, 5, 35, 215, 1295, 7775, 46655, 279935, 1679615, 10077695, 60466175, 362797055, 2176782335, 13060694015, 78364164095, 470184984575, 2821109907455, 16926659444735, 101559956668415, 609359740010495, 3656158440062975, 21936950640377855, 131621703842267135

Offset

0,2

Comments

In base 6 these are 0, 5, 55, 555, ... - David Rabahy, Dec 12 2016

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

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 (7,-6).

Formula

G.f.: 1/(1 - 6*x) - 1/(1 - x). - Mohammad K. Azarian, Jan 14 2009

E.g.f.: exp(6*x) - exp(x). - Mohammad K. Azarian, Jan 14 2009

a(n+1) = 6*a(n) + 5, with a(0) = 0. - Reinhard Zumkeller, Nov 22 2009

a(n) = Sum_{i = 1..n} 5^i*binomial(n, n - i) for n > 0, a(0) = 0. - Bruno Berselli, Nov 11 2015

Sum_{n>=1} 1/a(n) = A248723. - Amiram Eldar, Nov 13 2020

Mathematica

6^Range[0, 19] - 1 (* Alonso del Arte, Feb 22 2019 *)

Prog

(Magma) [6^n-1: n in [0..25]]; // Vincenzo Librandi, Jul 03 2011
(PARI) a(n)=6^n-1 \\ Charles R Greathouse IV, Dec 12 2016
(Scala) ((List.fill(24)(6L)).scanLeft(1L)(_ * _)).map(_ - 1L) // Alonso del Arte, Feb 22 2019

Crossrefs

Cf. A000400, A002279, A248723.

Sequence in context: A356391 A221578 A320071 * A180250 A002074 A187444

Adjacent sequences: A024059 A024060 A024061 * A024063 A024064 A024065

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved