login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A105055 a(n) = bitwise AND operation applied between every term of the n-th row of Pascal's triangle, with the stipulation that all bits left of the last significant bit in each element are turned "on" until all elements of a row contain the same number of bits (see example). Results represented in decimal notation. 0
1, 1, 2, 3, 4, 8, 20, 33, 64, 64, 192, 256, 768, 1024, 2304, 4353, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194034, 8388608, 16777216, 33554432, 67108864, 134217728, 268435457, 536870912, 1073741824, 2147483648 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For many n, a(n) = 2^k, where k = floor(log_2(A001405(n))). For n from 9 through 40, k = n-3, but it is smaller thereafter; no formula of the form k = n-c will work for sufficiently large n. There are infinitely many exceptions to this formula, since a(2^m-1) is always odd, hence not equal to 2^k for m > 1. - Franklin T. Adams-Watters, Mar 29 2014, replacing assertions by the author.

LINKS

Table of n, a(n) for n=0..34.

Eric Weisstein's World of Mathematics, Pascal's Triangle

Eric Weisstein's World of Mathematics, Bitwise AND

EXAMPLE

Consider the n = 7 row of Pascal's Triangle:

in decimal notation: 1-7-21-35-35-21-7-1;

in binary notation: 1-111-10101-100011-...

Note: only distinct digits are of any importance.

Now add 1's to the left of the most significant digit and "AND" all terms:

111111 AND 111111 AND 110101 AND 100011 = 100001

which is 33 in decimal, thus a(7)=33.

PROG

(PARI) nexttwo(n)=local(r=1); while(r<=n, r*=2); r

a(n)={local(v=vector(ceil(n/2), i, binomial(n, i)), r);

   r=nexttwo(v[#v])-1;

   for(i=1, #v, r=bitand(r, nexttwo(v[#v])-nexttwo(v[i])+v[i]));

r} \\ Franklin T. Adams-Watters, Mar 29 2014

CROSSREFS

Cf. A001405.

Sequence in context: A215897 A276673 A282815 * A108506 A129284 A214700

Adjacent sequences:  A105052 A105053 A105054 * A105056 A105057 A105058

KEYWORD

nonn,base

AUTHOR

Andrew G. West (WestA(AT)wlu.edu), Apr 04 2005

EXTENSIONS

Edited by Franklin T. Adams-Watters, Mar 29 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 7 03:42 EDT 2020. Contains 333292 sequences. (Running on oeis4.)