A024075 a(n) = 7^n-1.
0, 6, 48, 342, 2400, 16806, 117648, 823542, 5764800, 40353606, 282475248, 1977326742, 13841287200, 96889010406, 678223072848, 4747561509942, 33232930569600, 232630513987206, 1628413597910448, 11398895185373142
Offset: 0
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).
Programs
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Magma
[7^n-1: n in [0..25]]; // Vincenzo Librandi, Jul 03 2011
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Mathematica
CoefficientList[Series[1/(1 - 7 x) - 1/(1 - x), {x, 0, 19}], x] (* Michael De Vlieger, Jan 04 2020 *) -
Maxima
makelist(7^n-1, n, 0, 30); /* Martin Ettl, Nov 12 2012 */
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PARI
a(n)=7^n-1 \\ Charles R Greathouse IV, Dec 12 2016
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
Comments