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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

Table of n, a(n) for n=0..119.

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.)