A125682 a(n) = (6^n - 1)*3/5.

3, 21, 129, 777, 4665, 27993, 167961, 1007769, 6046617, 36279705, 217678233, 1306069401, 7836416409, 47018498457, 282110990745, 1692665944473, 10155995666841, 60935974001049, 365615844006297, 2193695064037785, 13162170384226713, 78973022305360281

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

Cf. A000400, A003464, A005610, A125687, A024062, A105281, A146884.

Sequence in context: A273803 A036754 A121447 * A357783 A360626 A274586

Adjacent sequences: A125679 A125680 A125681 * A125683 A125684 A125685

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