cp's OEIS Frontend

A356605 Number of integer compositions of n into odd parts covering an interval of odd positive integers.

%I A356605 #13 Sep 01 2022 19:48:07
%S A356605 1,1,1,2,3,5,6,10,15,26,41,65,104,164,262,424,687,1112,1792,2898,4677,
%T A356605 7556,12197,19699,31836,51466,83234,134593,217674,352057,569452,
%U A356605 921165,1490173,2410784,3900288,6310436,10210358,16521108,26733020,43258086,69999295
%N A356605 Number of integer compositions of n into odd parts covering an interval of odd positive integers.
%e A356605 The a(1) = 1 through a(8) = 15 compositions:
%e A356605   (1)  (11)  (3)    (13)    (5)      (33)      (7)        (35)
%e A356605              (111)  (31)    (113)    (1113)    (133)      (53)
%e A356605                     (1111)  (131)    (1131)    (313)      (1133)
%e A356605                             (311)    (1311)    (331)      (1313)
%e A356605                             (11111)  (3111)    (11113)    (1331)
%e A356605                                      (111111)  (11131)    (3113)
%e A356605                                                (11311)    (3131)
%e A356605                                                (13111)    (3311)
%e A356605                                                (31111)    (111113)
%e A356605                                                (1111111)  (111131)
%e A356605                                                           (111311)
%e A356605                                                           (113111)
%e A356605                                                           (131111)
%e A356605                                                           (311111)
%e A356605                                                           (11111111)
%t A356605 nogapQ[m_]:=m=={}||Union[m]==Range[Min[m],Max[m]];
%t A356605 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], And@@OddQ/@#&&nogapQ[(#+1)/2]&]],{n,0,15}]
%Y A356605 These compositions are ranked by the intersection of A060142 and A356841.
%Y A356605 Before restricting to odds we have A107428, initial A107429.
%Y A356605 The not necessarily gapless version is A324969 (essentially A000045).
%Y A356605 The strict case is A332032.
%Y A356605 The initial case is A356604.
%Y A356605 The case of partitions is A356737, initial A053251 (ranked by A356232).
%Y A356605 A000041 counts partitions, compositions A011782.
%Y A356605 A066208 lists numbers with all odd prime indices, counted by A000009.
%Y A356605 A073491 lists numbers with gapless prime indices, initial A055932.
%Y A356605 Cf. A001227, A066205, A137921, A333217, A356224, A356846.
%K A356605 nonn
%O A356605 0,4
%A A356605 _Gus Wiseman_, Aug 31 2022
%E A356605 More terms from _Alois P. Heinz_, Sep 01 2022