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
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).
Programs
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Magma
[6^n-1: n in [0..25]]; // Vincenzo Librandi, Jul 03 2011
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Mathematica
6^Range[0, 19] - 1 (* Alonso del Arte, Feb 22 2019 *)
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PARI
a(n)=6^n-1 \\ Charles R Greathouse IV, Dec 12 2016
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Scala
((List.fill(24)(6L)).scanLeft(1L)( * )).map( - 1L) // _Alonso del Arte, Feb 22 2019
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
Comments