This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A049773 Triangular array T read by rows: if row n is r(1),...,r(m), then row n+1 is 2r(1)-1,...,2r(m)-1,2r(1),...,2r(m). 10
 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 7, 2, 6, 4, 8, 1, 9, 5, 13, 3, 11, 7, 15, 2, 10, 6, 14, 4, 12, 8, 16, 1, 17, 9, 25, 5, 21, 13, 29, 3, 19, 11, 27, 7, 23, 15, 31, 2, 18, 10, 26, 6, 22, 14, 30, 4, 20, 12, 28, 8, 24, 16, 32, 1, 33, 17, 49, 9, 41, 25, 57, 5, 37, 21, 53, 13, 45, 29, 61, 3, 35, 19 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS n-th row = (r(1),r(2),...,r(m)), where m=2^(n-1), satisfies r(r(k))=k for k=1,2,...,m and has exactly 2^[ n/2 ] solutions of r(k)=k. (The function r(k) reverses bits. Or rather, r(k)=revbits(k-1)+1. In a knockout competition with m players, arranging the competition brackets (see links) in r(k) order, where k is the rank of the player, ensures that highest ranked players cannot meet until the later stages of the competition.  None of the top 2^p ranked players can meet earlier than the p-th from last round of the competition.  At the same time the top ranked players in each match meet the highest ranked player possible consistent with this rule.  The sequence for the top ranked players meeting the lowest ranked player possible is A208569.  See also A131271. - Colin Hall, Jul 31 2011, Feb 29 2012 Row n contains one of A003407(2^(n-1)) non-averaging permutations of [2^(n-1)], i.e., a permutation of [2^(n-1)] without 3-term arithmetic progressions. - Alois P. Heinz, Dec 05 2017 LINKS Alois P. Heinz, Rows n = 1..13, flattened Eric Weisstein's World of Mathematics, Nonaveraging Sequence Wikipedia, Arithmetic progression Wikipedia, Bracket (tournament) EXAMPLE Triangle begins: 1; 1,  2; 1,  3, 2,  4; 1,  5, 3,  7, 2,  6,  4,  8; 1,  9, 5, 13, 3, 11,  7, 15, 2, 10,  6, 14, 4, 12,  8, 16; 1, 17, 9, 25, 5, 21, 13, 29, 3, 19, 11, 27, 7, 23, 15, 31, 2, 18, 10, 26, ... MAPLE T:= proc(n) option remember; `if`(n=1, 1,       [map(x->2*x-1, [T(n-1)])[], map(x->2*x, [T(n-1)])[]][])     end: seq(T(n), n=1..7);  # Alois P. Heinz, Oct 28 2011 MATHEMATICA row[1] = {1}; row[n_] := row[n] = Join[ 2*row[n-1] - 1, 2*row[n-1] ]; Flatten[ Table[ row[n], {n, 1, 7}]] (* Jean-François Alcover, May 03 2012 *) PROG (PARI) (a(n, k) = if( k<=0 || k>=n, 0, if( k%2, n\2) + a(n\2, k\2))); {T(n, k) = if( k<=0 || k>2^n/2, 0, 1 + a(2^n/2, k-1))}; /* Michael Somos, Oct 13 1999 */ (Haskell) a049773 n k = a049773_tabf !! (n-1) !! (k-1) a049773_row n = a049773_tabf !! (n-1) a049773_tabf = iterate f [1] where    f vs = (map (subtract 1) ws) ++ ws where ws = map (* 2) vs -- Reinhard Zumkeller, Mar 14 2015 CROSSREFS Sum of odd-indexed terms of n-th row gives A007582. Sum of even-indexed terms gives A049775. A030109 is another version. Cf. A131271. Cf. A088370. - Alois P. Heinz, Oct 28 2011 Cf. A208569. - Colin Hall, Feb 29 2012 Cf. A003407, A088208. Sequence in context: A003602 A265650 A181733 * A261401 A217669 A123021 Adjacent sequences:  A049770 A049771 A049772 * A049774 A049775 A049776 KEYWORD nonn,tabf,nice,look AUTHOR 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.

Last modified February 21 15:03 EST 2018. Contains 299414 sequences. (Running on oeis4.)