0,3

Maximal power of 2 dividing n-th Catalan number (A000108).

Row sums of triangle A128937 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), May 02 2007

a(n) = sum of (n+1)-th row terms of triangle A167364 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 01 2009]

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

Contribution from Omar E. Pol (info(AT)polprimos.com), Jul 21 2009: (Start)

If written as a triangle:

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;

...

It appears that rows converge to the Gould's sequence A001316.

(End)

a := n -> 2^(add(i, i=convert(n+1, base, 2))-1); [From Peter Luschny (peter(AT)luschny.de), May 01 2009]

(PARI) a(n)=if(n<1, 1, if(n%2, a(n/2-1/2), 2*a(n-1)))

a(n)=2^A048881(n)

This is Guy Steele's sequence GS(3, 5) (see A135416).

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009: (Start)

Equals first right hand column of triangle A160468.

Equals A160469(n+1)/A002425(n+1).

Cf. A160476.

(End)

Cf. A000079, A001316. [From Omar E. Pol (info(AT)polprimos.com), Jul 21 2009]

Cf. A167364 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 01 2009]

Sequence in context: A152227 A078660 A060177 this_sequence A130831 A151678 A151681

Adjacent sequences: A048893 A048894 A048895 this_sequence A048897 A048898 A048899

nonn,new

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)

New definition from N. J. A. Sloane (njas(AT)research.att.com), Mar 01 2008