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%I #11 Apr 01 2022 23:53:25
%S 0,0,2,1,4,5,3,7,8,9,6,11,12,13,14,10,16,17,18,19,20,15,22,23,24,25,
%T 26,27,21,29,30,31,32,33,34,35,28,37,38,39,40,41,42,43,44,36,46,47,48,
%U 49,50,51,52,53,54,45,56,57,58,59,60,61,62,63,64,65,55,67
%N Number of integer compositions y of n with exactly one nonfixed point y(i) != i.
%e The a(2) = 2 through a(8) = 8 compositions:
%e (2) (3) (4) (5) (6) (7) (8)
%e (1,1) (1,3) (1,4) (1,5) (1,6) (1,7)
%e (2,2) (3,2) (4,2) (5,2) (6,2)
%e (1,2,1) (1,1,3) (1,2,4) (1,2,5)
%e (1,2,2) (1,3,3) (1,4,3)
%e (2,2,3) (3,2,3)
%e (1,2,3,1) (1,2,1,4)
%e (1,2,3,2)
%t pnq[y_]:=Length[Select[Range[Length[y]],#!=y[[#]]&]];
%t Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],pnq[#]==1&]],{n,0,15}]
%Y Compositions with no nonfixed points are counted by A010054.
%Y The version for weak excedances is A177510.
%Y Compositions with no fixed points are counted by A238351.
%Y The version for fixed points is A240736.
%Y This is column k = 1 of A352523.
%Y A011782 counts compositions.
%Y A238349 counts compositions by fixed points, rank stat A352512.
%Y A352486 gives the nonfixed points of A122111, counted by A330644.
%Y A352513 counts nonfixed points in standard compositions.
%Y Cf. A008930, A088218, A098825, A114088, A115994, A219282, A238352, A238874, A350839.
%K nonn
%O 0,3
%A _Gus Wiseman_, Mar 29 2022
%E More terms from _Alois P. Heinz_, Mar 30 2022
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