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A170942 Take the permutations of lengths 1, 2, 3, ... arranged lexicographically, and replace each permutation with the number of its fixed points. 19
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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]

LINKS

Reinhard Zumkeller, Rows n=1..7 of triangle, flattened

FindStat - Combinatorial Statistic Finder, The number of fixed points of a permutation

EXAMPLE

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

PROG

(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

CROSSREFS

Cf. A030298, A030299.

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

Cf. A008291.

Sequence in context: A299070 A209599 A238347 * A002187 A124756 A113504

Adjacent sequences:  A170939 A170940 A170941 * A170943 A170944 A170945

KEYWORD

nonn,tabf

AUTHOR

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

EXTENSIONS

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

Keyword tabf added by Reinhard Zumkeller, Mar 29 2012

STATUS

approved

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Last modified October 16 16:53 EDT 2018. Contains 316270 sequences. (Running on oeis4.)