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A356846
Number of integer compositions of n into parts not covering an interval of positive integers.
4
0, 0, 0, 0, 2, 5, 11, 25, 57, 115, 236, 482, 978, 1986, 4003, 8033, 16150, 32402, 64943, 130207, 260805, 522123, 1045168, 2091722, 4185431, 8374100, 16753538, 33515122, 67042865, 134106640, 268246886, 536549760, 1073194999, 2146553011, 4293391411, 8587283895
OFFSET
0,5
FORMULA
a(n) = A011782(n) - A107428(n).
EXAMPLE
The a(0) = 0 through a(6) = 8 compositions:
. . . . (13) (14) (15)
(31) (41) (24)
(113) (42)
(131) (51)
(311) (114)
(141)
(411)
(1113)
(1131)
(1311)
(3111)
MATHEMATICA
gappyQ[m_]:=And[m!={}, Union[m]!=Range[Min[m], Max[m]]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], gappyQ]], {n, 0, 15}]
CROSSREFS
The complement is counted by A107428, initial A107429.
The case of partitions is A239955, ranked by A073492, initial A053251, complement A034296.
These compositions are ranked by A356842, complement A356841.
A000041 counts partitions, compositions A011782.
A066208 lists numbers with all odd prime indices, counted by A000009.
A073491 lists numbers with gapless prime indices, initial A055932.
Sequence in context: A228765 A006054 A106805 * A094981 A304969 A239812
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 03 2022
STATUS
approved