login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A115199 Parity of partitions of n, with 0 for even, 1 for odd. The definition follows. 2
0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The main array with 0 and 1 interchanged is A115198.

A partition of n is (here) called even, resp. odd, if the number of even parts is even, resp. odd. A partition with no (0) even part is therefore even.

The row length sequence of this triangle is p(n)=A000041(n) (number of partitions).

See the W. Lang link under A115198 for the first 10 rows where 0 and 1 should be swapped for this a(n,m) entry.

LINKS

Table of n, a(n) for n=0..80.

FORMULA

a(n,m)= 0 if sum(e(n,m,2*j),j=1..floor(n/2)) is even, else 1, with the exponents e(n,m,k) of the m-th partition of n in the A-St order; i.e. the sum of the exponents of the even parts of the partition (1^e(n,m,1),2^e(n,m,2),..., n^e(n,m,n)) is even iff a(n,m)=0.

EXAMPLE

[0];[1,0];[0,1,0];[1,0,0,1,0];[0,1,1,0,0,1,0];...

a(5,4)=0 because the 4-th partition of n=5, (1^1,2^2)=(1,2,2), in the A-St order, has an even number of even parts (the number of even parts is in fact 2).

CROSSREFS

Sequence in context: A164349 A094186 A003849 * A085242 A059620 A083651

Adjacent sequences:  A115196 A115197 A115198 * A115200 A115201 A115202

KEYWORD

nonn,easy,tabf

AUTHOR

Wolfdieter Lang, Feb 23 2006

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified November 27 20:36 EST 2014. Contains 250272 sequences.