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A060546 a(n) is 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. 10
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

1,1

COMMENTS

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

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..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.: (2x+2x^2)/(1-2x^2). - Ralf Stephan, Jul 15 2013

MAPLE

for n from 1 to 100 do printf(`%d, `, 2^ceil(n/2)) od:

MATHEMATICA

2^Ceiling[Range[50]/2] (* or *) With[{c=2^Range[25]}, Riffle[c, c]] (* Harvey P. Dale, Mar 05 2013 *)

PROG

(PARI) { for (n=1, 500, write("b060546.txt", n, " ", 2^ceil(n/2)); ) } \\ Harry J. Smith, Jul 06 2009

CROSSREFS

Cf. A016116, A008619.

Sequence in context: A152166 A016116 * A163403 A231208 A222955 A217208

Adjacent sequences:  A060543 A060544 A060545 * A060547 A060548 A060549

KEYWORD

easy,nice,nonn

AUTHOR

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

EXTENSIONS

More terms from James A. Sellers, Apr 04 2001

STATUS

approved

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Last modified September 24 18:54 EDT 2017. Contains 292433 sequences.