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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A036563 a(n) = 2^n-3. 53
-2, -1, 1, 5, 13, 29, 61, 125, 253, 509, 1021, 2045, 4093, 8189, 16381, 32765, 65533, 131069, 262141, 524285, 1048573, 2097149, 4194301, 8388605, 16777213, 33554429, 67108861, 134217725, 268435453, 536870909, 1073741821, 2147483645 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n+1) is the n-th number with exactly n 1's in binary representation. - Reinhard Zumkeller, Mar 06 2003

Berstein and Onn: "For every m = 3k+1, the Graver complexity of the vertex-edge incidence matrix of the complete bipirtite graph K(3,m) satisfies g(m) >= 2^(k+2)-3." - Jonathan Vos Post, Sep 15 2007

Row sums of triangle A135857. - Gary W. Adamson, Dec 01 2007

a(n) = A164874(n-1,n-2) for n>2. [Reinhard Zumkeller, Aug 29 2009]

Starting (1, 5, 13,...) = eigensequence of a triangle with A016777: (1, 4, 7, 10,...) as the left border and the rest 1's. - Gary W. Adamson, Jul 24 2010

An elephant sequence, see A175655. For the central square just one A[5] vector, with decimal value 186, leads to this sequence (n>=2). For the corner squares this vector leads to the companion sequence A123203. - Johannes W. Meijer, Aug 15 2010

First differences of A095264: A095264(n+1)-A095264(n)=a(n+2). - J. M. Bergot, May 13 2013

a(n+2) is given by the sum of n-th row of triangle of powers of 2: 1; 2 1 2; 4 2 1 2 4; 8 4 2 1 2 4 8; ... - Philippe Deléham, Feb 24 2014

Also, the decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 643", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. See A283508.- Robert Price, Mar 09 2017

a(n+3) is the value of the Ackermann function A(3,n) or ack(3,n). - Olivier Gérard, May 11 2018

LINKS

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

Yael Berstein, Shmuel Onn, The Graver Complexity of Integer Programming, arXiv:0709.1500 [math.CO], 2007.

Irving Kaplansky and John Riordan, The problem of the rooks and its applications, in Combinatorics, Duke Mathematical Journal, 13.2 (1946): 259-268. [Annotated scanned copy]

Irving Kaplansky and John Riordan, The problem of the rooks and its applications, Duke Mathematical Journal 13.2 (1946): 259-268. Sequence is on page 267.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

FORMULA

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

The sequence 1, 5, 13, ... has a(n) = 4*2^n-3. These are the partial sums of A151821. - Paul Barry, Aug 25 2003

a(n) = A118654(n-3, 6), for n > 2. - N. J. A. Sloane, Sep 29 2006

Row sums of triangle A130459 starting (1, 5, 13, 29, 61,...). - Gary W. Adamson, May 26 2007

Row sums of triangle A131112. - Gary W. Adamson, Jun 15 2007

Binomial transform of [1, 4, 4, 4,...] = (1, 5, 13, 29, 61...). - Gary W. Adamson, Sep 20 2007

a(n) = 2*StirlingS2(n,2) - 1, for n > 0. - Ross La Haye, Jul 05 2008

a(n) = A000079(n)-3. [Omar E. Pol, Dec 21 2008]

G.f.: 1/(1-2*x)-3/(1-x). E.g.f.: e^(2*x)-3*e^x. [Mohammad K. Azarian, Jan 14 2009]

For n >= 3, a(n) = 2<+>n, where operation <+> is defined in A206853. - Vladimir Shevelev, Feb 17 2012

a(n) = 3*a(n-1)-2*a(n-2)for n>1, a(0)=-2, a(1)=-1. - Philippe Deléham, Dec 23 2013

EXAMPLE

a(2) = 1;

a(3) = 2 + 1 + 2 = 5;

a(4) = 4 + 2 + 1 + 2 + 4 = 13;

a(5) = 8 + 4 + 2 + 1 + 2 + 4 + 8 = 29; etc. - Philippe Deléham, Feb 24 2014

MAPLE

A036563:=n->2^n-3; seq(A036563(n), n=0..30); # Wesley Ivan Hurt, Jun 26 2014

MATHEMATICA

a=1; lst={a}; k=4; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 15 2008 *)

Table[2^n - 3, {n, 0, 30}] (* Wesley Ivan Hurt, Jun 26 2014 *)

PROG

(Sage) [gaussian_binomial(n, 1, 2)-2 for n in xrange(0, 32)] # Zerinvary Lajos, May 31 2009

(MAGMA) [2^n-3: n in [0..40]]; // Vincenzo Librandi, May 09 2011

(PARI) a(n)= 2^n-3 \\ Charles R Greathouse IV, Dec 22 2011

CROSSREFS

Row sums of triangular array A027960. A column of A119725.

Cf. A081118, A130459, A131112, A050414, A050415, A135857, A000079, A016777, A283508.

Cf. A074877, A304370, A304371.

Sequence in context: A098315 A006704 A174986 * A025264 A245567 A204168

Adjacent sequences:  A036560 A036561 A036562 * A036564 A036565 A036566

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 21 21:42 EDT 2018. Contains 313957 sequences. (Running on oeis4.)