A350846 Number of integer partitions of n with at least two adjacent parts of quotient 2.

0, 0, 0, 1, 1, 2, 4, 5, 8, 12, 18, 25, 36, 48, 65, 89, 119, 157, 207, 269, 350, 448, 574, 729, 927, 1166, 1465, 1830, 2282, 2827, 3501, 4309, 5300, 6483, 7923, 9641, 11718, 14187, 17155, 20674, 24885, 29860, 35787, 42772, 51054, 60791, 72289, 85772, 101641

Offset

0,6

Links

Table of n, a(n) for n=0..48.

Example

The a(3) = 1 through a(9) = 12 partitions:
  (21)  (211)  (221)   (42)     (421)     (422)      (63)
               (2111)  (321)    (2221)    (521)      (621)
                       (2211)   (3211)    (3221)     (3321)
                       (21111)  (22111)   (4211)     (4221)
                                (211111)  (22211)    (5211)
                                          (32111)    (22221)
                                          (221111)   (32211)
                                          (2111111)  (42111)
                                                     (222111)
                                                     (321111)
                                                     (2211111)
                                                     (21111111)

Mathematica

Table[Length[Select[IntegerPartitions[n], MemberQ[Divide@@@Partition[#, 2, 1], 2]&]], {n, 0, 30}]

Crossrefs

The complement is counted by A350837, strict A350840.

The complimentary additive version is A350842, strict A350844.

These partitions are ranked by A350845, complement A350838.

A000041 = integer partitions.

A323092 = double-free integer partitions, ranked by A320340.

Cf. A000929, A003000, A003114, A018819, A045690, A045691, A116931, A120641, A154402, A323093, A342094, A342095, A342096, A342098.

Sequence in context: A188216 A238395 A116901 * A244487 A290962 A334522

Adjacent sequences: A350843 A350844 A350845 * A350847 A350848 A350849

Keyword

nonn

Author

Gus Wiseman, Jan 20 2022

Status

approved