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A277083 Irregular triangle read by rows: T(n,k) = number of size k subsets of S_n that remain unchanged by a rotation of 180 degrees. 1
1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 4, 3, 2, 1, 1, 8, 36, 120, 322, 728, 1428, 2472, 3823, 5328, 6728, 7728, 8092, 7728, 6728, 5328, 3823, 2472, 1428, 728, 322, 120, 36, 8, 1, 1, 8, 84, 504, 3178, 15512, 74788, 311144, 1252819, 4577328, 16087512, 52691408, 165911284 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

A permutation, p, can be thought of as a set of points (i, p(i)). If you plot all the points and rotate the picture by 180 degrees then you get a permutation back.

T(n,k) is the number of size k subsets of S_n that remain unchanged by a rotation of 180 degrees.

LINKS

Table of n, a(n) for n=0..51.

FORMULA

T(n,k) = Sum_( binomial( n! - R(n), i ) * binomial( R(n), k-2*i ) for i in [0..floor(k/2)] ) where R(n) = A037223(n).

EXAMPLE

For n = 3 and k = 3, the subsets unchanged by rotating 180 degrees are {213,132,123}, {231,312,123}, {321,132,213} and {321,231,312} so T(3,3) = 4.

Triangle starts:

1, 1;

1, 1;

1, 2, 1;

1, 2, 3, 4, 3, 2, 1;

CROSSREFS

Row lengths give A038507.

Cf. A037223.

Sequence in context: A054482 A208234 A092543 * A216222 A090282 A022910

Adjacent sequences:  A277080 A277081 A277082 * A277084 A277085 A277086

KEYWORD

nonn,tabf

AUTHOR

Christian Bean, Sep 28 2016

STATUS

approved

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Last modified February 23 00:03 EST 2018. Contains 299472 sequences. (Running on oeis4.)