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Another variant of Per Nørgård's "infinity sequence", cf. A004718: t(0) = 0; t(4*n) = t(n); t(4*n+1) = t(n) - 2; t(4*n+2) = -t(n) - 1; t(4*n+3) = t(n) + 2.
4

%I #15 Oct 06 2017 11:36:41

%S 0,-2,-1,2,-2,-4,1,0,-1,-3,0,1,2,0,-3,4,-2,-4,1,0,-4,-6,3,-2,1,-1,-2,

%T 3,0,-2,-1,2,-1,-3,0,1,-3,-5,2,-1,0,-2,-1,2,1,-1,-2,3,2,0,-3,4,0,-2,

%U -1,2,-3,-5,2,-1,4,2,-5,6,-2,-4,1,0,-4,-6,3,-2,1,-1

%N Another variant of Per Nørgård's "infinity sequence", cf. A004718: t(0) = 0; t(4*n) = t(n); t(4*n+1) = t(n) - 2; t(4*n+2) = -t(n) - 1; t(4*n+3) = t(n) + 2.

%C Per Nørgård's surname is also written as Noergaard;

%C example of a sequence sharing with A004718 some main characterizing properties, see link (chapter 7).

%D Yu Hin (Gary) Au, Christopher Drexler-Lemire, and Jeffrey Shallit, "Notes and note pairs in Norgard's infinity series", J. of Mathematics and Music (2017). DOI: http://dx.doi.org/10.1080/17459737.2017.1299807

%H Reinhard Zumkeller, <a href="/A255723/b255723.txt">Table of n, a(n) for n = 0..10000</a>

%H Christopher Drexler-Lemire, Jeffrey Shallit, <a href="http://arxiv.org/abs/1402.3091">Notes and Note-Pairs in Noergaard's Infinity Series</a>, arXiv:1402.3091 [math.CO], page 12f.

%H Jørgen Mortensen, <a href="http://www.pernoergaard.dk/eng/strukturer/uendelig/uene.html">"Is Per Nørgård's infinity series unique?"</a>

%o (Haskell)

%o a255723 n = a255723_list !! n

%o a255723_list = 0 : concat (transpose [map (subtract 2) a255723_list,

%o map (-1 -) a255723_list,

%o map (+ 2) a255723_list,

%o tail a255723_list])

%Y Cf. A004718, A256184, A087808, A085144.

%K sign

%O 0,2

%A _Reinhard Zumkeller_, Mar 19 2015