This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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 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. 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 15 07:46 EDT 2018. Contains 316204 sequences. (Running on oeis4.)