A350840 - OEIS

A350840

Number of strict integer partitions of n with no adjacent parts of quotient 2.

1, 1, 1, 1, 2, 3, 2, 4, 5, 6, 7, 8, 10, 13, 17, 19, 22, 25, 30, 35, 43, 52, 60, 70, 81, 93, 106, 122, 142, 166, 190, 216, 249, 287, 325, 371, 420, 479, 543, 617, 695, 784, 888, 1000, 1126, 1266, 1420, 1594, 1792, 2008, 2247, 2514, 2809, 3135, 3496, 3891, 4332

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OFFSET

0,5

LINKS

Table of n, a(n) for n=0..56.

EXAMPLE

The a(1) = 1 through a(13) = 13 partitions (A..D = 10..13):

1 2 3 4 5 6 7 8 9 A B C D

31 32 51 43 53 54 64 65 75 76

41 52 62 72 73 74 93 85

61 71 81 82 83 A2 94

431 432 91 92 B1 A3

531 532 A1 543 B2

541 641 651 C1

731 732 643

741 652

831 751

832

931

5431

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&And@@Table[#[[i-1]]/#[[i]]!=2, {i, 2, Length[#]}]&]], {n, 0, 30}]

CROSSREFS

The version for subsets of prescribed maximum is A045691.

The double-free case is A120641.

The non-strict case is A350837, ranked by A350838.

An additive version (differences) is A350844, non-strict A350842.

The non-strict complement is counted by A350846, ranked by A350845.

Versions for prescribed quotients:

= 2: A154402, sets A001511.

!= 2: A350840 (this sequence), sets A045691.

>= 2: A000929, sets A018819.

<= 2: A342095, non-strict A342094.

< 2: A342097, non-strict A342096, sets A045690.

> 2: A342098, sets A040039.

A000041 = integer partitions.

A000045 = sets containing n with all differences > 2.

A003114 = strict partitions with no successions, ranked by A325160.

A116931 = partitions with no successions, ranked by A319630.

A116932 = partitions with differences != 1 or 2, strict A025157.

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

A350839 = partitions with gaps and conjugate gaps, ranked by A350841.

Cf. A003000, A018819, A303362, A323093, A323094, A337135, A342191.

Sequence in context: A304745 A353853 A365384 * A176789 A308158 A325349

Adjacent sequences: A350837 A350838 A350839 * A350841 A350842 A350843

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 20 2022

STATUS

approved