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 A274575 For m=1,2,3,... write all the 2^m binary vectors of length m in increasing order, and replace each vector with (number of 1's) - (number of 0's). Start with an initial 0 for the empty vector. 0
 0, -1, 1, -2, 0, 0, 2, -3, -1, -1, 1, -1, 1, 1, 3, -4, -2, -2, 0, -2, 0, 0, 2, -2, 0, 0, 2, 0, 2, 2, 4, -5, -3, -3, -1, -3, -1, -1, 1, -3, -1, -1, 1, -1, 1, 1, 3, -3, -1, -1, 1, -1, 1, 1, 3, -1, 1, 1, 3, 1, 3, 3, 5, -6, -4, -4, -2, -4, -2, -2, 0, -4, -2, -2, 0, -2, 0, 0, 2, -4, -2, -2, 0, -2, 0, 0, 2, -2, 0, 0, 2, 0, 2, 2, 4, -4, -2, -2, 0, -2, 0, 0, 2, -2, 0, 0, 2, 0, 2, 2, 4, -2, 0, 0, 2, 0, 2, 2, 4, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS This is the sequence of To-And-Fro positions: Positions of all backward-forward combinations in lexicographical order when assigning -1 to a backward move and +1 to a forward move and starting at 0. -a(n) are the slopes of the different segments, from left to right, of the successive steps in the construction of the Takagi (a.k.a. Blancmange) function. - Javier Múgica, Dec 31 2017 LINKS FORMULA a(2*n + 1) = a(n) - 1; a(2*n + 2) = a(n) + 1. EXAMPLE Terms a(3) to a(6) correspond to the binary vectors 00, 01, 10, 11, which get replaced by -2, 0, 0, 2, respectively. Terms a(7) to a(14) correspond to the binary vectors 000, 001, ..., 111 which get replaced by -3, -1, ..., 3. a(0) = 0 a(1) = a('backward') = -1 a(2) = a('forward') = +1 a(3) = a('backward and backward') = -2 a(4) = a('backward and forward') = 0 a(5) = a('forward and backward') = 0 a(6) = a('forward and forward') = +2 a(7) = a('backward, backward and backward') = -3 a(8) = a('backward, backward and forward') = -1 PROG Basic   Dim a(2*k+2) a(0) = 0 For n = 0 To k   a(2 * n + 1) = a(n) - 1   a(2 * n + 2) = a(n) + 1 Next n CROSSREFS Cf. A037861. Sequence in context: A323886 A174739 A280542 * A203994 A285725 A215889 Adjacent sequences:  A274572 A274573 A274574 * A274576 A274577 A274578 KEYWORD sign,easy AUTHOR Hans G. Oberlack, Jun 28 2016 EXTENSIONS Edited by N. J. A. Sloane, Jul 27 2016 STATUS approved

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Last modified November 14 09:51 EST 2019. Contains 329111 sequences. (Running on oeis4.)