A329740 Number of compositions of n whose multiplicities are distinct and cover an initial interval of positive integers.

1, 1, 1, 1, 4, 7, 4, 10, 10, 10, 73, 196, 133, 379, 319, 379, 502, 805, 562, 1108, 13648, 51448, 51691, 115174, 140011, 178597, 203617, 329737, 292300, 456703, 456160, 608386, 633466, 898186, 823009, 39014392, 190352269, 266293795, 493345615, 834326995, 947714938

Offset

0,5

Comments

A composition of n is a finite sequence of positive integers with sum n.

Links

Table of n, a(n) for n=0..40.

Example

The a(1) = 1 through a(9) = 10 compositions:
  (1)  (2)  (3)  (4)      (5)      (6)      (7)      (8)      (9)
                 (1,1,2)  (1,1,3)  (1,1,4)  (1,1,5)  (1,1,6)  (1,1,7)
                 (1,2,1)  (1,2,2)  (1,4,1)  (1,3,3)  (1,6,1)  (1,4,4)
                 (2,1,1)  (1,3,1)  (4,1,1)  (1,5,1)  (2,2,4)  (1,7,1)
                          (2,1,2)           (2,2,3)  (2,3,3)  (2,2,5)
                          (2,2,1)           (2,3,2)  (2,4,2)  (2,5,2)
                          (3,1,1)           (3,1,3)  (3,2,3)  (4,1,4)
                                            (3,2,2)  (3,3,2)  (4,4,1)
                                            (3,3,1)  (4,2,2)  (5,2,2)
                                            (5,1,1)  (6,1,1)  (7,1,1)

Mathematica

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], Range[Length[Union[#]]]==Sort[Length/@Split[Sort[#]]]&]], {n, 0, 10}]

Crossrefs

The version allowing repeated multiplicities is A329741.

Complete compositions are A107429.

Compositions whose multiplicities are distinct are A242882.

Cf. A059966, A098504, A244164, A274174, A329739, A329766, A329748.

Sequence in context: A094692 A385447 A059139 * A110669 A106027 A101159

Adjacent sequences: A329737 A329738 A329739 * A329741 A329742 A329743

Keyword

nonn

Author

Gus Wiseman, Nov 21 2019

Extensions

a(21)-a(40) from Alois P. Heinz, Nov 21 2019

Status

approved