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 A060546 a(n) = 2^ceiling(n/2). 33
 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 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] E.g.f.: cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x). - Stefano Spezia, Feb 02 2023 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] (* 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). The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A029744 = {s(n), n>=1}, the numbers 2^k and 3*2^k, as the parent: A029744 (s(n)); A052955 (s(n)-1), A027383 (s(n)-2), A354788 (s(n)-3), A347789 (s(n)-4), A209721 (s(n)+1), A209722 (s(n)+2), A343177 (s(n)+3), A209723 (s(n)+4); A060482, A136252 (minor differences from A354788 at the start); A354785 (3*s(n)), A354789 (3*s(n)-7). The first differences of A029744 are 1,1,1,2,2,4,4,8,8,... which essentially matches eight sequences: A016116, A060546, A117575, A131572, A152166, A158780, A163403, A320770. The bisections of A029744 are A000079 and A007283. - N. J. A. Sloane, Jul 14 2022 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

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Last modified March 31 16:04 EDT 2023. Contains 361668 sequences. (Running on oeis4.)