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A037800
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Number of occurrences of 01 in the binary expansion of n.
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12
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0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 1, 2, 2, 2, 1, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1
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OFFSET
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0,22
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COMMENTS
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Number of i such that d(i)>d(i-1), where Sum{d(i)*2^i: i=0,1,...,m} is base 2 representation of n.
This is the base-2 up-variation sequence; see A297330. - Clark Kimberling, Jan 18 2017
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
Eric Weisstein's World of Mathematics, Digit Block.
Index entries for sequences related to binary expansion of n
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FORMULA
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a(2n) = a(n), a(2n+1) = a(n) + [n is even]. - Ralf Stephan, Aug 21 2003
G.f.: 1/(1-x) * sum(k>=0, t^5/(1+t)/(1+t^2), t=x^2^k). - Ralf Stephan, Sep 10 2003
a(n) = A069010(n) - 1, n>0. - Ralf Stephan, Sep 10 2003
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PROG
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(Haskell)
a037800 = f 0 . a030308_row where
f c [_] = c
f c (1 : 0 : bs) = f (c + 1) bs
f c (_ : bs) = f c bs
-- Reinhard Zumkeller, Feb 20 2014
(PARI)
a(n) = { if(n == 0, 0, -1 + hammingweight(bitnegimply(n, n>>1))) }; \\ Gheorghe Coserea, Aug 31 2015
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CROSSREFS
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Cf. A014081, A014082, A033264, A056974, A056975, A056976, A056977, A056978, A056979, A056980.
Cf. A030308.
Sequence in context: A005590 A142598 A274372 * A144411 A138253 A261447
Adjacent sequences: A037797 A037798 A037799 * A037801 A037802 A037803
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KEYWORD
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nonn,base,easy
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AUTHOR
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Clark Kimberling
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STATUS
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approved
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