A199115 a(n) = 5*4^n+1.

6, 21, 81, 321, 1281, 5121, 20481, 81921, 327681, 1310721, 5242881, 20971521, 83886081, 335544321, 1342177281, 5368709121, 21474836481, 85899345921, 343597383681, 1374389534721, 5497558138881, 21990232555521, 87960930222081

Offset: 0

Author

Vincenzo Librandi, Nov 04 2011

Keywords

• nonn
• easy

Comments

An Engel expansion of 4/5 to the base 4 as defined in A181565, with the associated series expansion 4/5 = 4/6 + 4^2/(6*21) + 4^3/(6*21*81) + 4^4/(6*21*81*321) + ... . Cf. A136412 and A140660. - Peter Bala, Oct 29 2013

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

Cf. A136412, A140660, A199115.

Programs

Magma

[5*4^n+1: n in [0..30]];

Mathematica

5*4^Range[0,30]+1 (* or  *) LinearRecurrence[{5,-4},{6,21},30] (* Harvey P. Dale, Oct 19 2024 *)

Formula

a(n) = 3*A136412(n).

a(n) = 4*a(n-1)-3.

a(n) = 5*a(n-1)-4*a(n-2).

G.f.: 3*(2-3*x)/((1-x)*(1-4*x)). - Bruno Berselli, Nov 04 2011