cp's OEIS Frontend

A352520 Number of integer compositions y of n with exactly one nonfixed point y(i) != i.

%I A352520 #11 Apr 01 2022 23:53:25
%S A352520 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 A352520 26,27,21,29,30,31,32,33,34,35,28,37,38,39,40,41,42,43,44,36,46,47,48,
%U A352520 49,50,51,52,53,54,45,56,57,58,59,60,61,62,63,64,65,55,67
%N A352520 Number of integer compositions y of n with exactly one nonfixed point y(i) != i.
%e A352520 The a(2) = 2 through a(8) = 8 compositions:
%e A352520   (2)    (3)  (4)      (5)      (6)    (7)        (8)
%e A352520   (1,1)       (1,3)    (1,4)    (1,5)  (1,6)      (1,7)
%e A352520               (2,2)    (3,2)    (4,2)  (5,2)      (6,2)
%e A352520               (1,2,1)  (1,1,3)         (1,2,4)    (1,2,5)
%e A352520                        (1,2,2)         (1,3,3)    (1,4,3)
%e A352520                                        (2,2,3)    (3,2,3)
%e A352520                                        (1,2,3,1)  (1,2,1,4)
%e A352520                                                   (1,2,3,2)
%t A352520 pnq[y_]:=Length[Select[Range[Length[y]],#!=y[[#]]&]];
%t A352520 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],pnq[#]==1&]],{n,0,15}]
%Y A352520 Compositions with no nonfixed points are counted by A010054.
%Y A352520 The version for weak excedances is A177510.
%Y A352520 Compositions with no fixed points are counted by A238351.
%Y A352520 The version for fixed points is A240736.
%Y A352520 This is column k = 1 of A352523.
%Y A352520 A011782 counts compositions.
%Y A352520 A238349 counts compositions by fixed points, rank stat A352512.
%Y A352520 A352486 gives the nonfixed points of A122111, counted by A330644.
%Y A352520 A352513 counts nonfixed points in standard compositions.
%Y A352520 Cf. A008930, A088218, A098825, A114088, A115994, A219282, A238352, A238874, A350839.
%K A352520 nonn
%O A352520 0,3
%A A352520 _Gus Wiseman_, Mar 29 2022
%E A352520 More terms from _Alois P. Heinz_, Mar 30 2022