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A059905
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Index of first half of decomposition of integers into pairs based on A000695.
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27
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0, 1, 0, 1, 2, 3, 2, 3, 0, 1, 0, 1, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 6, 7, 4, 5, 4, 5, 6, 7, 6, 7, 0, 1, 0, 1, 2, 3, 2, 3, 0, 1, 0, 1, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 6, 7, 4, 5, 4, 5, 6, 7, 6, 7, 8, 9, 8, 9, 10, 11, 10, 11, 8, 9, 8, 9, 10, 11, 10, 11, 12, 13, 12, 13, 14, 15, 14, 15, 12, 13, 12, 13, 14
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OFFSET
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0,5
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COMMENTS
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One coordinate of a recursive non-self-intersecting walk on the square lattice Z^2.
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LINKS
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Peter Kagey, Table of n, a(n) for n = 0..8192
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FORMULA
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n = A000695(a(n)) + 2*A000695(A059906(n)).
To get a(n), write n as Sum b_j*2^j, then a(n) = Sum b_(2j)*2^j. - Vladimir Shevelev, Nov 13 2008
a(n) = Sum_{k>=0} A030308(n,k)*A077957(k). - Philippe Deléham, Oct 18 2011
G.f.: (1-x)^(-1) * Sum_{j>=0} 2^j*x^(2^j)/(1+x^(2^j)). - Robert Israel, Aug 12 2015
a(n) = A059906(2*n). - Velin Yanev, Dec 01 2016
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EXAMPLE
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A000695(a(14)) + 2*A000695(A059906(14)) = A000695(2) + 2*A000695(3) = 4 + 2*5 = 14.
If n=27, then b_0=1, b_1=1, b_2=0, b_3=1, b_4=1. Therefore a(n) = b_0 + b_2*2 + b_4*2^2 = 5. - Vladimir Shevelev, Nov 13 2008
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MAPLE
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f:= proc(n) local L; L:= convert(n, base, 2); add(L[2*i+1]*2^i, i=0..floor((nops(L)-1)/2)) end;
map(f, [$0..256]); # Robert Israel, Aug 12 2015
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MATHEMATICA
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a[n_] := Module[{P}, (P = Partition[IntegerDigits[2n, 2]//Reverse, 2][[All, 2]]).(2^(Range[Length[P]]-1))]; Array[a, 100, 0] (* Jean-François Alcover, Apr 24 2019 *)
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PROG
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(Ruby)
def a(n)
(0..n.bit_length/2).to_a.map { |i| (n >> 2 * i & 1) << i}.reduce(:+)
end # Peter Kagey, Aug 12 2015
(Python)
def a(n): return sum([(n>>2*i&1)<<i for i in xrange(int(len(bin(n)[2:])/2) + 1)])
print [a(n) for n in xrange(101)] # Indranil Ghosh, Jun 25 2017, after Ruby code by Peter Kagey
(PARI) A059905(n) = { my(t=1, s=0); while(n>0, s += (n%2)*t; n \= 4; t *= 2); (s); }; \\ Antti Karttunen, Apr 14 2018
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CROSSREFS
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Cf. A000695, A030308, A059906, A057300, A077957.
Sequence in context: A105436 A266911 A244075 * A295301 A308133 A306426
Adjacent sequences: A059902 A059903 A059904 * A059906 A059907 A059908
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KEYWORD
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easy,nonn,look
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AUTHOR
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Marc LeBrun, Feb 07 2001
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STATUS
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approved
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