cp's OEIS Frontend

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

%I A198380 #34 Apr 01 2012 14:16:09
%S A198380 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 A198380 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 A198380 6,4,5,6,4,6,2,4,5,6,2,4,1,2,3,4,4,6
%N A198380 Cycle type of the n-th finite permutation represented by index number of A194602.
%C A198380 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 A198380 From the properties of A194602 follows:
%C A198380 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 A198380 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 A198380 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 A198380 (Compare "Table for A194602" in section LINKS. Concerning the first two properties see especially the end of this file.)
%H A198380 Tilman Piesk, <a href="/A198380/b198380.txt">Table of n, a(n) for n = 0..5039</a>
%H A198380 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 A198380 Tilman Piesk, <a href="http://en.wikiversity.org/wiki/Permutations_by_cycle_structure">Permutations by cycle type</a> (Wikiversity article)
%H A198380 Tilman Piesk, <a href="https://oeis.org/A194602/a194602.txt">Table for A194602</a>
%Y A198380 Cf. A195663, A195664, A055089 (ordered finite permutations).
%Y A198380 Cf. A194602 (ordered partitions interpreted as binary numbers).
%Y A198380 Cf. A181897 (number of n-permutations with cycle type k).
%K A198380 nonn
%O A198380 0,4
%A A198380 _Tilman Piesk_, Oct 23 2011
%E A198380 Changed offset to 0 by Tilman Piesk, Jan 25 2012