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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A060546 a(n) = 2^ceiling(n/2). 13
1, 2, 2, 4, 4, 8, 8, 16, 16, 32, 32, 64, 64, 128, 128, 256, 256, 512, 512, 1024, 1024, 2048, 2048, 4096, 4096, 8192, 8192, 16384, 16384, 32768, 32768, 65536, 65536, 131072, 131072, 262144, 262144, 524288, 524288, 1048576, 1048576, 2097152, 2097152 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is also the number of median-reflective (palindrome) symmetric patterns in a top-down equilateral triangular arrangement of closely packed black and white cells satisfying the local matching rule of Pascal's triangle modulo 2, where n is the number of cells in each edge of the arrangement. The matching rule is such that any elementary top-down triangle of three neighboring cells in the arrangement contains either one or three white cells.

The number of possibilities for an n-game (sub)set of tennis with neither player gaining a 2-game advantage. (Motivated by the marathon Isner-Mahut match at Wimbledon, 2010.) - Barry Cipra, Jun 28 2010

Number of achiral rows of n colors using up to two colors. For a(3)=4, the rows are AAA, ABA, BAB, and BBB. - Robert A. Russell, Nov 07 2018

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..500

A. Barbé, Symmetric patterns in the cellular automaton that generates Pascal's triangle modulo 2, Discr. Appl. Math. 105(2000), 1-38.

Index entries for sequences related to cellular automata

Index to divisibility sequences

Index entries for linear recurrences with constant coefficients, signature (0,2).

FORMULA

a(n) = 2^ceiling(n/2).

a(n) = A016116(n+1) for n >= 1.

a(n) = 2^A008619(n-1) for n >= 1.

G.f.: (1+2*x) / (1-2*x^2). - Ralf Stephan, Jul 15 2013 [Adapted to offset 0 by Robert A. Russell, Nov 07 2018]

MAPLE

for n from 0 to 100 do printf(`%d, `, 2^ceil(n/2)) od:

MATHEMATICA

2^Ceiling[Range[0, 50]/2] (* or *) Riffle[2^Range[0, 25], 2^Range[25]] (* Harvey P. Dale, Mar 05 2013 *)

LinearRecurrence[{0, 2}, {1, 2}, 40] (* Robert A. Russell, Nov 07 2018 *)

PROG

(PARI) { for (n=0, 500, write("b060546.txt", n, " ", 2^ceil(n/2)); ) } \\ Harry J. Smith, Jul 06 2009

(MAGMA) [2^Ceiling(n/2): n in [0..50]]; // G. C. Greubel, Nov 07 2018

CROSSREFS

Column k=2 of A321391.

Cf. A016116, A008619.

Cf. A000079 (oriented), A005418(n+1) (unoriented), A122746(n-2) (chiral).

Sequence in context: A152166 A320770 A016116 * A163403 A231208 A306663

Adjacent sequences:  A060543 A060544 A060545 * A060547 A060548 A060549

KEYWORD

easy,nonn

AUTHOR

André Barbé (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 03 2001

EXTENSIONS

More terms from James A. Sellers, Apr 04 2001

a(0)=1 prepended by Robert A. Russell, Nov 07 2018

Edited by N. J. A. Sloane, Nov 10 2018

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 19 00:12 EST 2019. Contains 329310 sequences. (Running on oeis4.)