

A277085


Irregular triangle read by rows: T(n,k) = number of size k subsets of S_n that remain unchanged by a rotation of 90 degrees.


1



1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 2, 4, 6, 10, 14, 20, 26, 31, 36, 40, 44, 44, 44, 40, 36, 31, 26, 20, 14, 10, 6, 4, 2, 1, 1, 2, 4, 6, 34, 62, 116, 170, 547, 924, 1624, 2324, 5572, 8820, 14616, 20412, 40509, 60606, 95004, 129402, 224406, 319410
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OFFSET

0,16


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 90 degrees then you get a permutation back.
T(n,k) is the number of size k subsets that remain unchanged by a rotation of 90 degrees.


LINKS

Table of n, a(n) for n=0..60.


FORMULA

T(n,k) = Sum_( C( R(n)  T(n), i ) * Sum_(C(n!  R(n), j) * C(T(n), k  4*i  2*j) for j in [0..floor((k4*i)/2)] for i in [0..floor(k/4)] ) where R(n) = A037223(n) and T(n) = A037224(n).


EXAMPLE

For n = 4 and k = 2, the subsets unchanged by a 90 degree rotation are {4321,1234}, {4231,1324}, {3412,2143} and {3142,2413}. Hence T(4,2) = 4.
Triangle starts:
1, 1;
1, 1;
1, 0, 1;
1, 0, 1, 0, 1, 0, 1;


CROSSREFS

Row lengths give A038507.
Cf. A037223, A037224.
Sequence in context: A082379 A167379 A213476 * A094589 A071425 A115065
Adjacent sequences: A277082 A277083 A277084 * A277086 A277087 A277088


KEYWORD

nonn,tabf


AUTHOR

Christian Bean, Sep 28 2016


STATUS

approved



