cp's OEIS Frontend

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

%I A329739 #10 Jul 06 2020 19:22:22
%S A329739 1,1,2,2,5,8,10,20,28,41,62,102,124,208,278,426,571,872,1158,1718,
%T A329739 2306,3304,4402,6286,8446,11725,15644,21642,28636,38956,52296,70106,
%U A329739 93224,124758,165266,218916,290583,381706,503174,659160,865020,1124458,1473912,1907298
%N A329739 Number of compositions of n whose run-lengths are all different.
%C A329739 A composition of n is a finite sequence of positive integers with sum n.
%e A329739 The a(1) = 1 through a(7) = 20 compositions:
%e A329739   (1)  (2)   (3)    (4)     (5)      (6)       (7)
%e A329739        (11)  (111)  (22)    (113)    (33)      (115)
%e A329739                     (112)   (122)    (114)     (133)
%e A329739                     (211)   (221)    (222)     (223)
%e A329739                     (1111)  (311)    (411)     (322)
%e A329739                             (1112)   (1113)    (331)
%e A329739                             (2111)   (3111)    (511)
%e A329739                             (11111)  (11112)   (1114)
%e A329739                                      (21111)   (1222)
%e A329739                                      (111111)  (2221)
%e A329739                                                (4111)
%e A329739                                                (11113)
%e A329739                                                (11122)
%e A329739                                                (22111)
%e A329739                                                (31111)
%e A329739                                                (111112)
%e A329739                                                (111211)
%e A329739                                                (112111)
%e A329739                                                (211111)
%e A329739                                                (1111111)
%t A329739 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@Length/@Split[#]&]],{n,0,10}]
%Y A329739 The normal case is A329740.
%Y A329739 The case of partitions is A098859.
%Y A329739 Strict compositions are A032020.
%Y A329739 Compositions with relatively prime run-lengths are A000740.
%Y A329739 Compositions with distinct multiplicities are A242882.
%Y A329739 Compositions with distinct differences are A325545.
%Y A329739 Compositions with equal run-lengths are A329738.
%Y A329739 Compositions with normal run-lengths are A329766.
%Y A329739 Cf. A003242, A008965, A059966, A098504, A098859, A107429, A175342, A238130, A328592, A329745.
%K A329739 nonn
%O A329739 0,3
%A A329739 _Gus Wiseman_, Nov 20 2019
%E A329739 a(21)-a(26) from _Giovanni Resta_, Nov 22 2019
%E A329739 a(27)-a(43) from _Alois P. Heinz_, Jul 06 2020