cp's OEIS Frontend

A356737 Number of integer partitions of n into odd parts covering an interval of odd numbers.

%I A356737 #6 Sep 03 2022 12:19:54
%S A356737 1,1,1,2,2,3,3,4,4,6,6,7,8,9,10,13,13,15,17,19,21,25,26,29,33,37,40,
%T A356737 46,49,54,61,66,72,81,87,97,106,115,125,139,150,163,179,193,210,232,
%U A356737 248,269,293,317,343,373,401,433,470,507,545,590,633,682,737,790
%N A356737 Number of integer partitions of n into odd parts covering an interval of odd numbers.
%e A356737 The a(1) = 1 through a(9) = 6 partitions:
%e A356737   1  11  3    31    5      33      7        53        9
%e A356737          111  1111  311    3111    331      3311      333
%e A356737                     11111  111111  31111    311111    531
%e A356737                                    1111111  11111111  33111
%e A356737                                                       3111111
%e A356737                                                       111111111
%t A356737 nogapQ[m_]:=Or[m=={},Union[m]==Range[Min[m],Max[m]]];
%t A356737 Table[Length[Select[IntegerPartitions[n],And@@OddQ/@#&&nogapQ[(#+1)/2]&]],{n,0,30}]
%Y A356737 The strict case is A034178, for compositions A332032.
%Y A356737 The initial case is A053251, ranked by A356232 and A356603.
%Y A356737 The initial case for compositions is A356604.
%Y A356737 The version for compositions is A356605, ranked by A060142 /\ A356841.
%Y A356737 A000041 counts partitions, compositions A011782.
%Y A356737 A066208 lists numbers with all odd prime indices, counted by A000009.
%Y A356737 A073491 lists gapless numbers, initial A055932.
%Y A356737 Cf. A001227, A066205, A107428, A107429, A333217, A356224, A356846.
%K A356737 nonn
%O A356737 0,4
%A A356737 _Gus Wiseman_, Sep 03 2022