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A328187 Number of integer partitions of n with no pair of consecutive parts relatively prime. 12
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..59.

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: A083711 A018783 A200976 * A331885 A298971 A328602

Adjacent sequences:  A328184 A328185 A328186 * A328188 A328189 A328190

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 12 2019

STATUS

approved

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Last modified April 8 12:50 EDT 2020. Contains 333314 sequences. (Running on oeis4.)