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A115201 Number of even parts of partitions of n in the Abromowitz-Stegun (A-St) order. 1
0, 1, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 1, 1, 0, 2, 1, 0, 1, 0, 2, 0, 1, 1, 3, 0, 2, 1, 0, 0, 1, 1, 1, 0, 2, 0, 2, 1, 1, 3, 0, 2, 1, 0, 1, 0, 2, 0, 2, 1, 1, 1, 3, 1, 0, 2, 0, 2, 4, 1, 1, 3, 0, 2, 1, 0, 0, 1, 1, 1, 1, 0, 2, 0, 2, 2, 2, 0, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

A conjugacy class of the symmetric group S_n with the cycle structure given by the partition, listed in the A-St order, consists of even, resp. odd, permutations if a(n,m) is even, resp. odd.

See A115198 for the parity of a(n,m) with 1 for even, 0 for odd (main entry).

See A115199 for the parity of a(n,m) with 0 for even, 1 for odd.

The parity of these numbers determines whether a conjugacy class of the symmetric group S_n, which is determined by its cycle structure, consists of even or odd permutations.

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

LINKS

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

W. Lang: First 10 rows.

FORMULA

a(n,m)= sum(e(n,m,2*j),j=1..floor(n/2)) 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)).

EXAMPLE

[0];[1, 0];[0, 1, 0];[1, 0, 2, 1, 0];[0, 1, 1, 0, 2, 1, 0];...

CROSSREFS

The sequence of row lengths is A066898 (total number of even parts in all partitions of n).

Sequence in context: A303942 A321928 A321917 * A118229 A172250 A309047

Adjacent sequences:  A115198 A115199 A115200 * A115202 A115203 A115204

KEYWORD

nonn,easy,tabf

AUTHOR

Wolfdieter Lang, Feb 23 2006

STATUS

approved

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Last modified September 17 03:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)