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A170942 Take the permutations of lengths 1, 2, 3, ... arranged lexicographically, and replace each permutation by the number of its fixed points. 19

%I

%S 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,

%T 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,

%U 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

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

%C 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]

%H Reinhard Zumkeller, <a href="/A170942/b170942.txt">Rows n=1..7 of triangle, flattened</a>

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/St000022">The number of fixed points of a permutation</a>

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

%o (Haskell)

%o import Data.List (permutations, sort)

%o a170942 n k = a170942_tabf !! (n-1) (k-1)

%o a170942_row n = map fps $ sort $ permutations [1..n] where

%o fps perm = sum $ map fromEnum $ zipWith (==) perm [1..n]

%o a170942_tabf = map a170942_row [1..]

%o -- _Reinhard Zumkeller_, Mar 29 2012

%Y Cf. A030298, A030299.

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

%Y Cf. A008291.

%K nonn,tabf

%O 1,2

%A Neven Juric (neven.juric(AT)apis-it.hr) and _N. J. A. Sloane_, Feb 23 2010

%E a(36)-a(105) from _John W. Layman_, Feb 23 2010

%E Keyword tabf added by _Reinhard Zumkeller_, Mar 29 2012

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Last modified April 18 19:33 EDT 2014. Contains 240733 sequences.