A024075 - OEIS

%I #39 Feb 16 2024 10:09:24

%S 0,6,48,342,2400,16806,117648,823542,5764800,40353606,282475248,

%T 1977326742,13841287200,96889010406,678223072848,4747561509942,

%U 33232930569600,232630513987206,1628413597910448,11398895185373142

%N a(n) = 7^n-1.

%C In base 7 these are 0, 6, 66, 666, ... - _David Rabahy_, Dec 12 2016

%H Vincenzo Librandi, <a href="/A024075/b024075.txt">Table of n, a(n) for n = 0..500</a>

%H Amelia Carolina Sparavigna, <a href="https://doi.org/10.5281/zenodo.3471358">The groupoids of Mersenne, Fermat, Cullen, Woodall and other Numbers and their representations by means of integer sequences</a>, Politecnico di Torino, Italy (2019), [math.NT].

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-7).

%F G.f.: 1/(1-7*x)-1/(1-x). - _Mohammad K. Azarian_, Jan 14 2009

%F E.g.f.: exp(7*x)-exp(x). - _Mohammad K. Azarian_, Jan 14 2009

%F a(n+1) = 7*a(n) + 6. - _Reinhard Zumkeller_, Nov 22 2009

%F a(n) = Sum_{i=1..n} 6^i*binomial(n,n-i) for n>0, a(0)=0. - _Bruno Berselli_, Nov 11 2015

%F a(n) = A000420(n) - 1. - _Sean A. Irvine_, Jun 19 2019

%F Sum_{n>=1} 1/a(n) = A248724. - _Amiram Eldar_, Nov 13 2020

%t CoefficientList[Series[1/(1 - 7 x) - 1/(1 - x), {x, 0, 19}], x] (* _Michael De Vlieger_, Jan 04 2020 *)

%o (Magma) [7^n-1: n in [0..25]]; // _Vincenzo Librandi_, Jul 03 2011

%o (Maxima) makelist(7^n-1, n, 0, 30); /* _Martin Ettl_, Nov 12 2012 */

%o (PARI) a(n)=7^n-1 \\ _Charles R Greathouse IV_, Dec 12 2016

%Y Cf. A000420, A248724.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.