A328187 Number of integer partitions of n with no pair of consecutive parts relatively prime.

1, 1, 1, 1, 2, 1, 4, 1, 5, 3, 8, 1, 14, 1, 16, 9, 22, 3, 38, 4, 46, 19, 58, 9, 94, 18, 106, 41, 144, 28, 221, 37, 246, 92, 318, 87, 465, 95, 530, 198, 693, 169, 963, 220, 1108, 424, 1383, 381, 1899, 492, 2216, 815, 2732, 799, 3644, 1041, 4231, 1585, 5194, 1608

Offset

0,5

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..300

Example

The a(1) = 1 through a(15) = 9 partitions (A..F = 10..15):
  1  2  3  4   5  6    7  8     9    A      B  C       D  E        F
           22     33      44    63   55        66         77       96
                  42      62    333  64        84         86       A5
                  222     422        82        93         A4       C3
                          2222       442       A2         C2       555
                                     622       444        644      663
                                     4222      633        662      933
                                     22222     642        842      6333
                                               822        A22      33333
                                               3333       4442
                                               4422       6422
                                               6222       8222
                                               42222      44222
                                               222222     62222
                                                          422222
                                                          2222222

Mathematica

Table[Length[Select[IntegerPartitions[n], !MatchQ[#, {___, x_, y_, ___}/; GCD[x, y]==1]&]], {n, 0, 30}]

Crossrefs

The Heinz numbers of these partitions are given by A328336.

The case of compositions is A178470.

The strict case is A328220.

Partitions with all pairs of consecutive parts relatively prime are A328172.

Cf. A000837, A018783, A328028, A328170, A328171, A328188.

Sequence in context: A339619 A018783 A200976 * A331885 A298971 A328602

Adjacent sequences: A328184 A328185 A328186 * A328188 A328189 A328190

Keyword

nonn

Author

Gus Wiseman, Oct 12 2019

Status

approved