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

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, 26, 27, 21, 29, 30, 31, 32, 33, 34, 35, 28, 37, 38, 39, 40, 41, 42, 43, 44, 36, 46, 47, 48, 49, 50, 51, 52, 53, 54, 45, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 55, 67

Offset

0,3

Links

Table of n, a(n) for n=0..67.

Example

The a(2) = 2 through a(8) = 8 compositions:
  (2)    (3)  (4)      (5)      (6)    (7)        (8)
  (1,1)       (1,3)    (1,4)    (1,5)  (1,6)      (1,7)
              (2,2)    (3,2)    (4,2)  (5,2)      (6,2)
              (1,2,1)  (1,1,3)         (1,2,4)    (1,2,5)
                       (1,2,2)         (1,3,3)    (1,4,3)
                                       (2,2,3)    (3,2,3)
                                       (1,2,3,1)  (1,2,1,4)
                                                  (1,2,3,2)

Mathematica

pnq[y_]:=Length[Select[Range[Length[y]], #!=y[[#]]&]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], pnq[#]==1&]], {n, 0, 15}]

Crossrefs

Compositions with no nonfixed points are counted by A010054.

The version for weak excedances is A177510.

Compositions with no fixed points are counted by A238351.

The version for fixed points is A240736.

This is column k = 1 of A352523.

A011782 counts compositions.

A238349 counts compositions by fixed points, rank stat A352512.

A352486 gives the nonfixed points of A122111, counted by A330644.

A352513 counts nonfixed points in standard compositions.

Cf. A008930, A088218, A098825, A114088, A115994, A219282, A238352, A238874, A350839.

Sequence in context: A239806 A330402 A075302 * A350313 A257911 A257882

Adjacent sequences: A352517 A352518 A352519 * A352521 A352522 A352523

Keyword

nonn

Author

Gus Wiseman, Mar 29 2022

Extensions

More terms from Alois P. Heinz, Mar 30 2022

Status

approved