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Search: id:A048896
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| 1, 1, 2, 1, 2, 2, 4, 1, 2, 2, 4, 2, 4, 4, 8, 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Maximal power of 2 dividing n-th Catalan number (A000108).
Row sums of triangle A128937 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), May 02 2007
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FORMULA
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a(n) = 2^k if 2^k divides A000108(n) but 2^(k+1) does not divide A000108(n).
It appears that a(n) = sum( binomial(2*(n+1), k) mod 2, k=0..n ). - Christopher Lenard (c.lenard(AT)bendigo.latrobe.edu.au), Aug 20 2001
a(0)=1; a(2n)=2*a(2n-1); a(2n+1)=a(n)
a(n)=(1/2)*A001316(n+1) - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 26 2004
It appears that a(n)=sum{k=0..2n, floor(C(2n+2, k+1)/2)(-1)^k}=2^n-sum{k=0..n+1, floor(C(n+1, k)/2} - Paul Barry (pbarry(AT)wit.ie), Dec 24 2004
a(n)=Sum (T(n,k) mod 2, k=0..n) where T=A039598, A053121, A052179, A124575, A126075, A126093 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), May 02 2007
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PROGRAM
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(PARI) a(n)=if(n<1, 1, if(n%2, a(n/2-1/2), 2*a(n-1)))
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CROSSREFS
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a(n)=2^A048881(n)
This is Guy Steele's sequence GS(3,5) (see A135416).
Sequence in context: A003113 A078660 A060177 this_sequence A130831 A131097 A062790
Adjacent sequences: A048893 A048894 A048895 this_sequence A048897 A048898 A048899
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KEYWORD
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nonn
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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EXTENSIONS
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New definition from njas, Mar 01 2008
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