A356846 Number of integer compositions of n into parts not covering an interval of positive integers.

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

Author

Gus Wiseman, Sep 03 2022

Keywords

• nonn

Examples

			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)
		

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.

Cf. A001227, A060142, A080259, A188575, A239327, A356604, A356605.

Programs

Mathematica

gappyQ[m_]:=And[m!={},Union[m]!=Range[Min[m],Max[m]]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],gappyQ]],{n,0,15}]

Formula

a(n) = A011782(n) - A107428(n).