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 A188037 a(n) = floor(nr) - 1 - floor((n-1)r), where r = sqrt(2). 6

%I

%S 0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,

%T 0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,

%U 0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0

%N a(n) = floor(nr) - 1 - floor((n-1)r), where r = sqrt(2).

%C Is this A159684 with an additional 0 in front? - _R. J. Mathar_, Mar 20 2011

%C The answer is yes, since it follows right from the definitions of the sequences that (a(n)) is equal to A159684 with a different offset. - _Michel Dekking_, Jan 31 2017

%H Vincenzo Librandi, <a href="/A188037/b188037.txt">Table of n, a(n) for n = 1..5000</a>

%H Heinz H. Bauschke, Minh N. Dao, Scott B. Lindstrom, <a href="https://arxiv.org/abs/1804.08880">The Douglas-Rachford algorithm for a hyperplane and a doubleton</a>, arXiv:1804.08880 [math.OC], 2018.

%F a(n) = floor(nr) - floor(r) - floor(nr - r), where r = sqrt(2).

%t r=2^(1/2)); k=1;

%t t=Table[Floor[n*r]-Floor[(n-k)*r]-Floor[k*r],{n,1,220}]

%t Table[Floor[n Sqrt[2]] - Floor[Sqrt[2]] - Floor[n Sqrt[2] - Sqrt[2]], {n, 100}] (* _Vincenzo Librandi_, Jan 31 2017 *)

%o (MAGMA) [Floor(n*Sqrt(2))-Floor(Sqrt(2))-Floor(n*Sqrt(2)- Sqrt(2)): n in [1..100]]; // _Vincenzo Librandi_, Jan 31 2017

%o (PARI) a(n) = floor(n*sqrt(2))-1-floor((n-1)*sqrt(2)) \\ _Felix FrÃ¶hlich_, Jan 31 2017

%Y Cf. A080754, A083088, A188014, A188037, A188038.

%Y A159684 is an essentially identical sequence.

%K nonn

%O 1

%A _Clark Kimberling_, Mar 19 2011

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Last modified April 19 10:39 EDT 2019. Contains 322255 sequences. (Running on oeis4.)