A170942 Take the permutations of lengths 1, 2, 3, ... arranged lexicographically, and replace each permutation with the number of its fixed points.

1, 2, 0, 3, 1, 1, 0, 0, 1, 4, 2, 2, 1, 1, 2, 2, 0, 1, 0, 0, 1, 1, 0, 2, 1, 0, 0, 0, 1, 1, 2, 0, 0, 5, 3, 3, 2, 2, 3, 3, 1, 2, 1, 1, 2, 2, 1, 3, 2, 1, 1, 1, 2, 2, 3, 1, 1, 3, 1, 1, 0, 0, 1, 2, 0, 1, 0, 0, 1, 1, 0, 2, 1, 0, 0, 0, 1, 1, 2, 0, 0, 2, 0, 1, 0, 0, 1, 3, 1, 2, 1, 1, 2, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0

Offset: 1

Author

Neven Juric (neven.juric(AT)apis-it.hr) and N. J. A. Sloane, Feb 23 2010

Keywords

• nonn
• tabf

Comments

Length of n-th row = sum of n-th row = n!; number of zeros in n-th row = A000166(n); number of positive terms in n-th row = A002467(n). [Reinhard Zumkeller, Mar 29 2012]

Examples

			123,132,213,231,312,321 (corresponding to 3rd row of triangle A030298) have respectively 3,1,1,0,0,1 fixed points.
		

Links

• Reinhard Zumkeller, Rows n=1..7 of triangle, flattened
• FindStat - Combinatorial Statistic Finder, The number of fixed points of a permutation

Crossrefs

Cf. A030298, A030299.

Cf. A008290, A000166, A000240, A000387, A000449, A000475, A129135, A129136, A129149, A129153, A129217, A129218, A129238, A129255.

Cf. A008291.

Programs

Haskell

import Data.List (permutations, sort)
a170942 n k = a170942_tabf !! (n-1) (k-1)
a170942_row n = map fps $ sort $ permutations [1..n] where
   fps perm = sum $ map fromEnum $ zipWith (==) perm [1..n]
a170942_tabf = map a170942_row [1..]
-- Reinhard Zumkeller, Mar 29 2012

Extensions

a(36)-a(105) from John W. Layman, Feb 23 2010

Keyword tabf added by Reinhard Zumkeller, Mar 29 2012