This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A211362 #10 Jun 08 2012 20:15:32
%S A211362 0,1,4,3,6,7,32,33,20,11,22,15,48,41,52,43,30,31,56,57,60,59,62,63,
%T A211362 512,513,516,515,518,519,288,289,148,75,150,79,304,297,180,107,158,95,
%U A211362 312,313,188,123,190,127,768,769,644,579,646,583,800
%N A211362 Inversion sets of finite permutations interpreted as binary numbers.
%C A211362 Each finite permutation has a finite inversion set. The possible elements of the inversion sets are 2-element subsets of the integers, which can be ordered in an infinite sequence (compare A018900). Thus the inversion set can be represented by a binary vector, which can be interpreted as a binary number.
%C A211362 This sequence shows these numbers for the finite permutations in reverse colexicographic order (A055089, A195663). The corresponding inversion vectors are found in A007623. The corresponding inversion numbers (A034968) are the digit sums of the inversion vectors and the cardinality of the inversion sets, an thus also the binary digit sums of the numbers in this sequence.
%C A211362 This sequence is not monotonic. The permutation A211363 shows how the elements of this sequence (a) are ordered. a*A211363 gives the elements of a ordered by size.
%H A211362 Tilman Piesk, <a href="/A211362/b211362.txt">Table of n, a(n) for n = 0..5039</a>
%H A211362 Wikipedia, <a href="http://en.wikipedia.org/wiki/Inversion_%28discrete_mathematics%29">Inversion (discrete mathematics)</a>
%e A211362 The 4th finite permutation (2,3,1,4,...) has the inversion set {(1,3),(2,3)}. This set represented by a vector is (0,1,1,zeros...). This vector interpreted as a number is 6. So a(4)=6.
%e A211362 The 23rd finite permutation (4,3,2,1,...) has the inversion set {(1,2),(1,3),(2,3),(1,4),(2,4),(3,4)}. This set represented by a vector is (1,1,1,1,1,1,zeros...). This vector interpreted as a number is 63. So a(23)=63.
%e A211362 Beginning of corresponding array:
%e A211362 n permutation inversion set a(n)
%e A211362 00 1 2 3 4 0 0 0 0 0 0 0
%e A211362 01 2 1 3 4 1 0 0 0 0 0 1
%e A211362 02 1 3 2 4 0 0 1 0 0 0 4
%e A211362 03 3 1 2 4 1 1 0 0 0 0 3
%e A211362 04 2 3 1 4 0 1 1 0 0 0 6
%e A211362 05 3 2 1 4 1 1 1 0 0 0 7
%e A211362 06 1 2 4 3 0 0 0 0 0 1 32
%e A211362 07 2 1 4 3 1 0 0 0 0 1 33
%e A211362 08 1 4 2 3 0 0 1 0 1 0 20
%e A211362 09 4 1 2 3 1 1 0 1 0 0 11
%e A211362 10 2 4 1 3 0 1 1 0 1 0 22
%e A211362 11 4 2 1 3 1 1 1 1 0 0 15
%e A211362 12 1 3 4 2 0 0 0 0 1 1 48
%e A211362 13 3 1 4 2 1 0 0 1 0 1 41
%e A211362 14 1 4 3 2 0 0 1 0 1 1 52
%e A211362 15 4 1 3 2 1 1 0 1 0 1 43
%e A211362 16 3 4 1 2 0 1 1 1 1 0 30
%e A211362 17 4 3 1 2 1 1 1 1 1 0 31
%e A211362 18 2 3 4 1 0 0 0 1 1 1 56
%e A211362 19 3 2 4 1 1 0 0 1 1 1 57
%e A211362 20 2 4 3 1 0 0 1 1 1 1 60
%e A211362 21 4 2 3 1 1 1 0 1 1 1 59
%e A211362 22 3 4 2 1 0 1 1 1 1 1 62
%e A211362 23 4 3 2 1 1 1 1 1 1 1 63
%Y A211362 Cf. A018900, A055089, A195663, A034968, A211363.
%K A211362 nonn
%O A211362 0,3
%A A211362 _Tilman Piesk_, Jun 03 2012