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%I #22 Jan 01 2017 02:04:27
%S 0,1,3,2,4,5,11,10,8,9,7,6,12,13,15,14,16,17,23,22,20,21,19,18,93,92,
%T 94,95,90,91,78,79,81,80,82,83,89,88,86,87,85,84,74,75,73,72,77,76,52,
%U 53,48,49,51,50,71,70,68,69,67,66,55,54,59,58
%N a(n) is the n-th permutation generated by Heap's algorithm, represented by row number of A055089.
%C This is a permutation of the nonnegative integers. It divides naturally in sections of factorial length, so it can be seen as a triangle with row lengths A094258:
%C 0,
%C 1,
%C 3, 2, 4, 5,
%C 11, 10, 8, 9, 7, 6, 12, 13, 15, 14, 16, 17, 23, 22, 20, 21, 19, 18...
%C Compare A280319 for Steinhaus-Johnson-Trotter algorithm, which is a triangle of finite permutations rather than one infinite permutation.
%H Tilman Piesk, <a href="/A280318/b280318.txt">Table of n, a(n) for n = 0..5039</a>
%H Tilman Piesk, <a href="http://pastebin.com/ERqb4EaX">Calculation in Python</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Heap's_algorithm">Heap's algorithm</a>
%e Example for the first 24 entries of the sequence. On the right are the permutations of {1,2,3,4} in the order generated by the Heap's algorithm:
%e n rev colex a(n) Heap's
%e 0 1 2 3 4 0 1 2 3 4
%e 1 2 1 3 4 1 2 1 3 4
%e 2 1 3 2 4 3 3 1 2 4
%e 3 3 1 2 4 2 1 3 2 4
%e 4 2 3 1 4 4 2 3 1 4
%e 5 3 2 1 4 5 3 2 1 4
%e 6 1 2 4 3 11 4 2 1 3
%e 7 2 1 4 3 10 2 4 1 3
%e 8 1 4 2 3 8 1 4 2 3
%e 9 4 1 2 3 9 4 1 2 3
%e 10 2 4 1 3 7 2 1 4 3
%e 11 4 2 1 3 6 1 2 4 3
%e 12 1 3 4 2 12 1 3 4 2
%e 13 3 1 4 2 13 3 1 4 2
%e 14 1 4 3 2 15 4 1 3 2
%e 15 4 1 3 2 14 1 4 3 2
%e 16 3 4 1 2 16 3 4 1 2
%e 17 4 3 1 2 17 4 3 1 2
%e 18 2 3 4 1 23 4 3 2 1
%e 19 3 2 4 1 22 3 4 2 1
%e 20 2 4 3 1 20 2 4 3 1
%e 21 4 2 3 1 21 4 2 3 1
%e 22 3 4 2 1 19 3 2 4 1
%e 23 4 3 2 1 18 2 3 4 1
%Y Cf. A055089, A094258, A280319.
%K nonn,tabf
%O 0,3
%A _Tilman Piesk_, Dec 31 2016