A125682 a(n) = 3*(6^n - 1)/5.
3, 21, 129, 777, 4665, 27993, 167961, 1007769, 6046617, 36279705, 217678233, 1306069401, 7836416409, 47018498457, 282110990745, 1692665944473, 10155995666841, 60935974001049, 365615844006297, 2193695064037785, 13162170384226713, 78973022305360281, 473838133832161689
Offset: 1
Examples
Base 6 Base 10 3 ............. 3 = 3*6^0 33 ........... 21 = 3*6^1 + 3*6^0 333 ......... 129 = 3*6^2 + 3*6^1 + 3*6^0 3333 ........ 777 = 3*6^3 + 3*6^2 + 3*6^1 + 3*6^0, etc.
Links
- Bruno Berselli, Table of n, a(n) for n = 1..1000
- Kival Ngaokrajang, Illustration of initial terms.
- Index entries for linear recurrences with constant coefficients, signature (7,-6).
Programs
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Magma
[(6^n-1)*3/5: n in [1..22]]; // Bruno Berselli, Apr 18 2012
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Maple
seq((6^n-1)*3/5, n=1..27);
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Mathematica
a[n_]:=(6^n-1)*3/5; Table[a[n],{n,1,22}] (* Robert P. P. McKone, Aug 29 2023 *)
Formula
G.f.: 3*x/((1-x)*(1-6*x)). - Bruno Berselli, Apr 18 2012
a(n) = 7*a(n-1) - 6*a(n-2). - Wesley Ivan Hurt, Dec 25 2021
From Elmo R. Oliveira, Mar 29 2025: (Start)
E.g.f.: 3*exp(x)*(exp(5*x) - 1)/5.
a(n) = 3*A003464(n). (End)
Extensions
Edited by N. J. A. Sloane, Feb 02 2007
Definition rewritten (with Lajos formula) from Bruno Berselli, Apr 18 2012
Comments