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A134931 a(n) = (5*3^n-3)/2. 15
1, 6, 21, 66, 201, 606, 1821, 5466, 16401, 49206, 147621, 442866, 1328601, 3985806, 11957421, 35872266, 107616801, 322850406, 968551221, 2905653666, 8716961001, 26150883006, 78452649021, 235357947066, 706073841201, 2118221523606 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Numbers n where the recurrence s(0)=1, if s(n-1) >= n then s(n) = s(n-1) - n else s(n) = s(n-1) + n produces s(n)=0. - Hugo Pfoertner, Jan 05 2012

A046901(a(n)) = 1. - Reinhard Zumkeller, Jan 31 2013

Binomial transform of A146523: (1, 5, 10, 20, 40,...) and double binomial transform of A010685: (1, 4, 1, 4, 1, 4,...). - Gary W. Adamson, Aug 25 2016

Also the number of maximal cliques in the (n+1)-Hanoi graph. - Eric W. Weisstein, Dec 01 2017

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Eric Weisstein's World of Mathematics, Hanoi Graph

Eric Weisstein's World of Mathematics, Maximal Clique

Index entries for linear recurrences with constant coefficients, signature (4,-3).

FORMULA

a(n) = 3*(a(n-1)+1), with a(0)=1.

O.g.f.: 5/2/(1-3*x)-3/2/(1-x). a(n) = (A005030(n)-3)/2. - R. J. Mathar, Jan 31 2008

a(n) = A060816(n+1)-1. - Philippe Deléham, Apr 14 2013

MAPLE

seq((5*3^n-3)/2, n= 0..25); # Gary Detlefs, Jun 22 2010

MATHEMATICA

a=1; lst={a}; Do[a=a*3+3; AppendTo[lst, a], {n, 0, 100}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 25 2008 *)

Table[(5 3^n - 9)/6, {n, 20}] (* Eric W. Weisstein, Dec 01 2017 *)

(5 3^Range[20] - 9)/6 (* Eric W. Weisstein, Dec 01 2017 *)

LinearRecurrence[{4, -3}, {1, 6}, 20] (* Eric W. Weisstein, Dec 01 2017 *)

CoefficientList[Series[(1 + 2 x)/(1 - 4 x + 3 x^2), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 01 2017 *)

PROG

(MAGMA) [(5*3^n-3)/2: n in [0..30]]; // Vincenzo Librandi, Jun 05 2011

(PARI) a(n) = (5*3^n-3)/2; /* Joerg Arndt, Apr 14 2013 */

CROSSREFS

Cf. A003462, A007051, A034472, A024023, A067771, A029858. - Vladimir Joseph Stephan Orlovsky, Dec 25 2008

Cf. A146523

Sequence in context: A320855 A117962 A105457 * A119103 A180795 A306089

Adjacent sequences:  A134928 A134929 A134930 * A134932 A134933 A134934

KEYWORD

nonn,easy

AUTHOR

Rolf Pleisch, Jan 29 2008

EXTENSIONS

More terms from Vladimir Joseph Stephan Orlovsky, Dec 25 2008

STATUS

approved

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Last modified November 14 16:49 EST 2018. Contains 317210 sequences. (Running on oeis4.)