login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A055010 a(0) = 0; for n > 0, 3*2^(n-1) - 1. 30
0, 2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, 196607, 393215, 786431, 1572863, 3145727, 6291455, 12582911, 25165823, 50331647, 100663295, 201326591, 402653183, 805306367, 1610612735 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Apart from leading term (which should really be 3/2), same as A083329.

Written in binary, a(n) is 1011111...1

The sequence 2,5,11,23,47,95,... apparently gives values of n such that Nim-factorial(n) = 2. Cf. A059970. However, compare A060152. More work is needed! - John W. Layman, Mar 09 2001

With offset 1, number of (132,3412)-avoiding two-stack sortable permutations.

Number of descents after n+1 iterations of morphism A007413.

a(n) = A164874(n,1), n>0; subsequence of A030130. [From Reinhard Zumkeller, Aug 29 2009]

Let A be the Hessenberg matrix of order n, defined by: A[1,j]=[i,i]:=1, A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=(-1)^n*charpoly(A,-1). [From Milan Janjic, Jan 24 2010]

a(n+1) = A196168(A000079(n)). [Reinhard Zumkeller, Oct 28 2011]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Thabit ibn Kurrah Number

E. S. Egge and T. Mansour, 132-avoiding two-stack sortable permutations..., arXiv:math.CO/0205206

S. Kitaev and T. Mansour, Counting the occurrences of generalized patterns..., arXiv:math.CO/0210170

Index to sequences with linear recurrences with constant coefficients, signature (3,-2).

FORMULA

a(n) = 2*a(n-1) + 1 = a(n-1) + A007283(n-1) = A007283(n)-1 = A000079(n) + A000225(n + 1) = A000079(n + 1) + A000225(n) = 3*A000079(n)-1 = 3*A000225(n) + 2.

a(n) = A010036(n)/2^(n-1) . - Philippe Deléham, Feb 20 2004

a(n) = A099258(A033484(n)-1) = floor(A033484(n)/2). - Reinhard Zumkeller, Oct 09 2004

a(n)=[ -1+3*2^(n-1)]*{1-[C(2*n,n) mod 2]}, with n>=0 [From Paolo P. Lava, Nov 20 2008]

G.f.: x*(2-x)/((1-x)*(1-2*x)). [From Philippe Deléham, Oct 04 2011]

EXAMPLE

a(3) = 3*2^2-1 = 3*4-1 = 11

MATHEMATICA

a=2; lst={0, a}; k=3; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 6!}]; lst [From Vladimir Joseph Stephan Orlovsky, Dec 15 2008]

Join[{0}, 3*2^Range[0, 30]-1] (* Harvey P. Dale, May 05 2013 *)

PROG

(MAGMA) [Floor(3*2^(n-1) - 1): n in [0..35]]; // Vincenzo Librandi, May 18 2011

CROSSREFS

Cf. A007505 for primes in this sequence. Apart from initial term, same as A052940 and A083329.

a(n) = A118654(n-1, 4), for n > 0.

Sequence in context: A133489 A060153 A086219 * A083329 A153893 A081973

Adjacent sequences:  A055007 A055008 A055009 * A055011 A055012 A055013

KEYWORD

easy,nonn

AUTHOR

Henry Bottomley, May 31 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 27 11:59 EST 2014. Contains 250196 sequences.