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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
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.
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((k-4*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.
Sequence in context: A082379 A167379 A213476 * A094589 A071425 A115065
KEYWORD
nonn,tabf
AUTHOR
Christian Bean, Sep 28 2016
STATUS
approved