OFFSET
1,1
COMMENTS
The base-6 numbers 3_6, 33_6, 333_6, 3333_6, 33333_6, 333333_6, ... converted to base 10.
Also the total number of holes in a certain triangle fractal (start with 6 triangles, 3 holes) after n iterations. See illustration in Ngaokrajang link. - Jens Ahlström, Aug 29 2023
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).
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
EXAMPLE
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.
MAPLE
seq((6^n-1)*3/5, n=1..27);
MATHEMATICA
a[n_]:=(6^n-1)*3/5; Table[a[n], {n, 1, 22}] (* Robert P. P. McKone, Aug 29 2023 *)
PROG
(Magma) [(6^n-1)*3/5: n in [1..22]]; // Bruno Berselli, Apr 18 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Jan 31 2007
EXTENSIONS
Edited by N. J. A. Sloane, Feb 02 2007
Definition rewritten (with Lajos formula) from Bruno Berselli, Apr 18 2012
STATUS
approved