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A024075 a(n) = 7^n-1. 12
0, 6, 48, 342, 2400, 16806, 117648, 823542, 5764800, 40353606, 282475248, 1977326742, 13841287200, 96889010406, 678223072848, 4747561509942, 33232930569600, 232630513987206, 1628413597910448, 11398895185373142 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Numbers n for which the expression 7^n/(n+1) is an integer. - Paolo P. Lava, May 29 2006

In base 7 these are 0, 6, 66, 666, ... - 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].

Index entries for linear recurrences with constant coefficients, signature (8,-7).

FORMULA

G.f.: 1/(1-7*x)-1/(1-x). - Mohammad K. Azarian, Jan 14 2009

E.g.f.: exp(7*x)-exp(x). - Mohammad K. Azarian, Jan 14 2009

a(n+1) = 7*a(n) + 6. - Reinhard Zumkeller, Nov 22 2009

a(n) = Sum_{i=1..n} 6^i*binomial(n,n-i) for n>0, a(0)=0. - Bruno Berselli, Nov 11 2015

a(n) = A000420(n) - 1. - Sean A. Irvine, Jun 19 2019

Sum_{n>=1} 1/a(n) = A248724. - Amiram Eldar, Nov 13 2020

MATHEMATICA

CoefficientList[Series[1/(1 - 7 x) - 1/(1 - x), {x, 0, 19}], x] (* Michael De Vlieger, Jan 04 2020 *)

PROG

(MAGMA) [7^n-1: n in [0..25]]; // Vincenzo Librandi, Jul 03 2011

(Maxima) makelist(7^n-1, n, 0, 30); /* Martin Ettl, Nov 12 2012 */

(PARI) a(n)=7^n-1 \\ Charles R Greathouse IV, Dec 12 2016

CROSSREFS

Cf. A000420, A248724.

Sequence in context: A300582 A049316 A320072 * A052571 A324074 A052625

Adjacent sequences:  A024072 A024073 A024074 * A024076 A024077 A024078

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified July 27 01:40 EDT 2021. Contains 346302 sequences. (Running on oeis4.)