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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 4th 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

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Last modified December 8 02:07 EST 2016. Contains 278902 sequences.