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 A198380 Cycle type of the n-th finite permutation represented by index number of A194602. 5

%I

%S 0,1,1,2,2,1,1,3,2,4,4,2,2,4,1,2,3,4,4,2,2,1,4,3,1,3,3,5,5,3,2,5,4,6,

%T 6,4,4,6,2,4,5,6,6,4,4,2,6,5,2,5,4,6,6,4,1,3,2,4,4,2,3,5,4,6,6,5,5,3,

%U 6,4,5,6,4,6,2,4,5,6,2,4,1,2,3,4,4,6

%N Cycle type of the n-th finite permutation represented by index number of A194602.

%C This sequence shows the cycle type of each finite permutation (A195663) as the index number of the corresponding partition. (When a permutation has a 3-cycle and a 2-cycle, this corresponds to the partition 3+2, etc.) Partitions can be ordered, so each partition can be denoted by its index in this order, e.g. 6 for the partition 3+2. Compare A194602.

%C From the properties of A194602 follows:

%C Entries 1,2,4,6,10,14,21... ( A000041(n)-1 from n=2 ) correspond to permutations with exactly one n-cycle (and no other cycles).

%C Entries 1,3,7,15,30,56,101... ( A000041(2n-1) from n=1 ) correspond to permutations with exactly n 2-cycles (and no other cycles), so these are the symmetric permutations.

%C Entries n = 1,3,4,7,9,10,12... ( A194602(n) has an even binary digit sum ) correspond to even permutations. This goes along with the fact, that a permutation is even when its partition contains an even number of even addends.

%C (Compare "Table for A194602" in section LINKS. Concerning the first two properties see especially the end of this file.)

%H Tilman Piesk, <a href="/A198380/b198380.txt">Table of n, a(n) for n = 0..5039</a>

%H Tilman Piesk, <a href="/A198380/a198380_1.txt">Table including permutations of 8 elements and partitions written as sums</a> for n = 0..40319

%H Tilman Piesk, <a href="http://en.wikiversity.org/wiki/Permutations_by_cycle_structure">Permutations by cycle type</a> (Wikiversity article)

%H Tilman Piesk, <a href="https://oeis.org/A194602/a194602.txt">Table for A194602</a>

%Y Cf. A195663, A195664, A055089 (ordered finite permutations).

%Y Cf. A194602 (ordered partitions interpreted as binary numbers).

%Y Cf. A181897 (number of n-permutations with cycle type k).

%K nonn

%O 0,4

%A _Tilman Piesk_, Oct 23 2011

%E Changed offset to 0 by Tilman Piesk, Jan 25 2012

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