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%I #11 Jan 22 2024 03:54:25
%S 0,1,1,1,2,1,1,2,1,1,2,1,2,2,1,1,2,2,3,2,2,1,2,2,1,2,2,2,3,2,1,2,1,1,
%T 2,1,2,2,1,1,2,2,3,2,2,1,2,2,2,3,2,2,3,2,1,2,1,1,2,1,2,2,2,2,2,2,3,2,
%U 3,2,2,2,3,3,2,2,3,3,2,2,1,1,2,2,2,2,2,2,2,2,3,3,3,3,2,2,4,3,3,2,3,3,3,2,2,1,2,2,3,2,3,2,2,2,3,3,3,3,2,2
%N a(n) is the number of elements p(j) < j (left displacements) in the n-th permutation in lexicographic order.
%H Joerg Arndt, <a href="/A369377/b369377.txt">Table of n, a(n) for n = 0..40319</a>
%F a(n) + A369376(n) = A055093(n).
%e In the following dots are used for zeros in the permutations and their inverses.
%e n: permutation inv. perm. a(n)
%e 0: [ . 1 2 3 ] [ . 1 2 3 ] 0
%e 1: [ . 1 3 2 ] [ . 1 3 2 ] 1
%e 2: [ . 2 1 3 ] [ . 2 1 3 ] 1
%e 3: [ . 2 3 1 ] [ . 3 1 2 ] 1
%e 4: [ . 3 1 2 ] [ . 2 3 1 ] 2
%e 5: [ . 3 2 1 ] [ . 3 2 1 ] 1
%e 6: [ 1 . 2 3 ] [ 1 . 2 3 ] 1
%e 7: [ 1 . 3 2 ] [ 1 . 3 2 ] 2
%e 8: [ 1 2 . 3 ] [ 2 . 1 3 ] 1
%e 9: [ 1 2 3 . ] [ 3 . 1 2 ] 1
%e 10: [ 1 3 . 2 ] [ 2 . 3 1 ] 2
%e 11: [ 1 3 2 . ] [ 3 . 2 1 ] 1
%e 12: [ 2 . 1 3 ] [ 1 2 . 3 ] 2
%e 13: [ 2 . 3 1 ] [ 1 3 . 2 ] 2
%e 14: [ 2 1 . 3 ] [ 2 1 . 3 ] 1
%e 15: [ 2 1 3 . ] [ 3 1 . 2 ] 1
%e 16: [ 2 3 . 1 ] [ 2 3 . 1 ] 2
%e 17: [ 2 3 1 . ] [ 3 2 . 1 ] 2
%e 18: [ 3 . 1 2 ] [ 1 2 3 . ] 3
%e 19: [ 3 . 2 1 ] [ 1 3 2 . ] 2
%e 20: [ 3 1 . 2 ] [ 2 1 3 . ] 2
%e 21: [ 3 1 2 . ] [ 3 1 2 . ] 1
%e 22: [ 3 2 . 1 ] [ 2 3 1 . ] 2
%e 23: [ 3 2 1 . ] [ 3 2 1 . ] 2
%Y Cf. A369376, A055093, A034968.
%K nonn
%O 0,5
%A _Joerg Arndt_, Jan 22 2024