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%I #54 Jun 30 2022 14:43:20
%S 0,0,1,1,0,0,1,1,2,2,3,3,2,2,3,3,0,0,1,1,0,0,1,1,2,2,3,3,2,2,3,3,4,4,
%T 5,5,4,4,5,5,6,6,7,7,6,6,7,7,4,4,5,5,4,4,5,5,6,6,7,7,6,6,7,7,0,0,1,1,
%U 0,0,1,1,2,2,3,3,2,2,3,3,0,0,1,1,0,0,1,1,2,2,3,3,2,2,3,3,4,4,5,5,4,4,5,5,6
%N Index of second half of decomposition of integers into pairs based on A000695.
%C One coordinate of a recursive non-self-intersecting walk on the square lattice Z^2.
%H Rémy Sigrist, <a href="/A059906/b059906.txt">Table of n, a(n) for n = 0..8192</a>
%H G. M. Morton, <a href="https://dominoweb.draco.res.ibm.com/0dabf9473b9c86d48525779800566a39.html">A Computer Oriented Geodetic Data Base; and a New Technique in File Sequencing</a>, IBM, 1966, with a(n) being section 5.1 step (b).
%H <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F n = A000695(A059905(n)) + 2*A000695(a(n))
%F To get a(n), write n as Sum b_j*2^j, then a(n) = Sum b_(2j+1)*2^j. - _Vladimir Shevelev_, Nov 13 2008
%F a(n) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=0 and b(k)=A077957(k-1) for k>0. - _Philippe Deléham_, Oct 18 2011
%F Conjecture: a(n) = n - (1/2)*Sum_{k=1..n} (sqrt(2)^A007814(k) + (-sqrt(2))^A007814(k)) = -Sum_{k=1..n} (-1)^k * 2^floor(k/2) * floor(n/2^k). - _Velin Yanev_, Dec 01 2016
%e A000695(A059905(14)) + 2*A000695(a(14)) = A000695(2) + 2*A000695(3) = 4 + 2*5 = 14.
%e If n=27, then b_0=1, b_1=1, b_2=0, b_3=1, b_4=1. Therefore a(27) = b_1 + b_3*2 = 3. - _Vladimir Shevelev_, Nov 13 2008
%t a[n_] := Module[{P}, (P = Partition[IntegerDigits[n, 2]//Reverse, 2][[All, 2]]).(2^(Range[Length[P]]-1))]; Array[a, 105, 0] (* _Jean-François Alcover_, Apr 24 2019 *)
%o (Python)
%o def a(n):
%o x=[int(t) for t in list(bin(n)[2:])[::-1]]
%o return sum(x[2*i + 1]*2**i for i in range(int(len(x)//2)))
%o print([a(n) for n in range(105)]) # _Indranil Ghosh_, Jun 25 2017
%o (Python)
%o def A059906(n): return 0 if n < 2 else int(bin(n)[-2:1:-2][::-1],2) # _Chai Wah Wu_, Jun 30 2022
%o (PARI) A059906(n) = { my(t=1,s=0); while(n>0, s += ((n%4)>=2)*t; n \= 4; t *= 2); (s); }; \\ _Antti Karttunen_, Apr 14 2018
%Y Cf. A000695, A057300, A059905.
%K easy,look,nonn
%O 0,9
%A _Marc LeBrun_, Feb 07 2001
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