A199108 a(n) = 4*3^n + 1.

5, 13, 37, 109, 325, 973, 2917, 8749, 26245, 78733, 236197, 708589, 2125765, 6377293, 19131877, 57395629, 172186885, 516560653, 1549681957, 4649045869, 13947137605, 41841412813, 125524238437, 376572715309, 1129718145925, 3389154437773, 10167463313317, 30502389939949

Offset: 0

Author

Vincenzo Librandi, Nov 03 2011

Keywords

• nonn
• easy

Comments

An Engel expansion of 3/4 to the base 3 as defined in A181565, with the associated series expansion 3/4 = 3/5 + 3^2/(5*13) + 3^3/(5*13*37) + 3^4/(5*13*37*109) + .... - 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 (4,-3).

Crossrefs

Cf. A181565.

Programs

Magma

[4*3^n+1 : n in [0..30]];

Mathematica

4*3^Range[0,30]+1 (* or *) LinearRecurrence[{4,-3},{5,13},30] (* or *) NestList[3#-2&,5,30] (* Harvey P. Dale, Mar 01 2012 *)

Formula

a(n) = 3*a(n-1) - 2.

a(n) = 4*a(n-1) - 3*a(n-2).

G.f.: (5-7*x)/((1-x)*(1-3*x)). - Bruno Berselli, Nov 03 2011

E.g.f.: exp(x)*(1 + 4*exp(2*x)). - Elmo R. Oliveira, May 07 2025