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A059906 Index of second half of decomposition of integers into pairs based on A000695. 17
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

One coordinate of a recursive non-self intersecting walk on the square lattice Z^2.

LINKS

Table of n, a(n) for n=0..104.

FORMULA

n = A000695(A059905(n)) + 2*A000695(a(n))

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

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

Conjecture: a(n) = n - Sum(k=1..n, sqrt(2)^A007814(k)+(-sqrt(2))^A007814(k))/2 = -Sum(k=1..n, (-1)^k * 2^floor(k/2) * floor(n/2^k)). - Velin Yanev, Dec 01 2016

EXAMPLE

A000695(A059905(14)) + 2*A000695(a(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_1 + b_3*2 = 3. - Vladimir Shevelev, Nov 13 2008

PROG

(Python)

def a(n):

    x=map(int, list(bin(n)[2:]))[::-1]

    return sum([x[2*i + 1]*2**i for i in xrange(int(len(x)/2))])

print [a(n) for n in xrange(105)] # Indranil Ghosh, Jun 25 2017

CROSSREFS

Cf. A000695, A059905.

Sequence in context: A213202 A234972 A130326 * A112046 A076902 A287271

Adjacent sequences:  A059903 A059904 A059905 * A059907 A059908 A059909

KEYWORD

easy,nonn

AUTHOR

Marc LeBrun, Feb 07 2001

STATUS

approved

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Last modified January 17 18:28 EST 2018. Contains 297829 sequences.