A329739 Number of compositions of n whose run-lengths are all different.

1, 1, 2, 2, 5, 8, 10, 20, 28, 41, 62, 102, 124, 208, 278, 426, 571, 872, 1158, 1718, 2306, 3304, 4402, 6286, 8446, 11725, 15644, 21642, 28636, 38956, 52296, 70106, 93224, 124758, 165266, 218916, 290583, 381706, 503174, 659160, 865020, 1124458, 1473912, 1907298

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..43.

Example

The a(1) = 1 through a(7) = 20 compositions:
  (1)  (2)   (3)    (4)     (5)      (6)       (7)
       (11)  (111)  (22)    (113)    (33)      (115)
                    (112)   (122)    (114)     (133)
                    (211)   (221)    (222)     (223)
                    (1111)  (311)    (411)     (322)
                            (1112)   (1113)    (331)
                            (2111)   (3111)    (511)
                            (11111)  (11112)   (1114)
                                     (21111)   (1222)
                                     (111111)  (2221)
                                               (4111)
                                               (11113)
                                               (11122)
                                               (22111)
                                               (31111)
                                               (111112)
                                               (111211)
                                               (112111)
                                               (211111)
                                               (1111111)

Mathematica

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@Length/@Split[#]&]], {n, 0, 10}]

Crossrefs

The normal case is A329740.

The case of partitions is A098859.

Strict compositions are A032020.

Compositions with relatively prime run-lengths are A000740.

Compositions with distinct multiplicities are A242882.

Compositions with distinct differences are A325545.

Compositions with equal run-lengths are A329738.

Compositions with normal run-lengths are A329766.

Cf. A003242, A008965, A059966, A098504, A098859, A107429, A175342, A238130, A328592, A329745.

Sequence in context: A286559 A183928 A333191 * A126291 A056224 A293674

Adjacent sequences: A329736 A329737 A329738 * A329740 A329741 A329742

Keyword

nonn

Author

Gus Wiseman, Nov 20 2019

Extensions

a(21)-a(26) from Giovanni Resta, Nov 22 2019

a(27)-a(43) from Alois P. Heinz, Jul 06 2020

Status

approved