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%I #39 Sep 08 2022 08:44:48
%S 0,5,35,215,1295,7775,46655,279935,1679615,10077695,60466175,
%T 362797055,2176782335,13060694015,78364164095,470184984575,
%U 2821109907455,16926659444735,101559956668415,609359740010495,3656158440062975,21936950640377855,131621703842267135
%N a(n) = 6^n - 1.
%C In base 6 these are 0, 5, 55, 555, ... - _David Rabahy_, Dec 12 2016
%H Vincenzo Librandi, <a href="/A024062/b024062.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 Amelia Carolina Sparavigna, <a href="https://doi.org/10.18483/ijSci.2188">Some Groupoids and their Representations by Means of Integer Sequences</a>, International Journal of Sciences (2019) Vol. 8, No. 10.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-6).
%F G.f.: 1/(1 - 6*x) - 1/(1 - x). - _Mohammad K. Azarian_, Jan 14 2009
%F E.g.f.: exp(6*x) - exp(x). - _Mohammad K. Azarian_, Jan 14 2009
%F a(n+1) = 6*a(n) + 5, with a(0) = 0. - _Reinhard Zumkeller_, Nov 22 2009
%F a(n) = Sum_{i = 1..n} 5^i*binomial(n, n - i) for n > 0, a(0) = 0. - _Bruno Berselli_, Nov 11 2015
%F Sum_{n>=1} 1/a(n) = A248723. - _Amiram Eldar_, Nov 13 2020
%t 6^Range[0, 19] - 1 (* _Alonso del Arte_, Feb 22 2019 *)
%o (Magma) [6^n-1: n in [0..25]]; // _Vincenzo Librandi_, Jul 03 2011
%o (PARI) a(n)=6^n-1 \\ _Charles R Greathouse IV_, Dec 12 2016
%o (Scala) ((List.fill(24)(6L)).scanLeft(1L)(_ * _)).map(_ - 1L) // _Alonso del Arte_, Feb 22 2019
%Y Cf. A000400, A002279, A248723.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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