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A199108 4*3^n+1. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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).

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

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 *)

PROG

(MAGMA) [4*3^n+1 : n in [0..30]]

CROSSREFS

A181565.

Sequence in context: A220709 A182312 A071100 * A125734 A146925 A146452

Adjacent sequences:  A199105 A199106 A199107 * A199109 A199110 A199111

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Nov 03 2011

STATUS

approved

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Last modified May 28 11:40 EDT 2020. Contains 334681 sequences. (Running on oeis4.)