A328220 Number of strict integer partitions of n with no pair of consecutive parts relatively prime.

1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 1, 5, 1, 5, 4, 6, 3, 10, 3, 11, 7, 12, 3, 19, 5, 18, 12, 23, 9, 36, 11, 33, 21, 40, 20, 58, 19, 58, 35, 70, 31, 98, 36, 101, 65, 112, 56, 155, 64, 164, 97, 188, 88, 250, 112, 256, 157, 293, 145, 392, 163, 399, 241, 461, 242

Offset

0,7

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..500

Example

The a(2) = 1 through a(20) = 11 partitions (A..K = 10..20):
  2  3  4  5  6   7  8   9   A   B  C    D  E    F   G    H    I    J    K
              42     62  63  64     84      86   96  A6   863  A8   964  C8
                             82     93      A4   A5  C4   962  C6   A63  E6
                                    A2      C2   C3  E2        E4        F5
                                    642     842      862       F3        G4
                                                     A42       G2        I2
                                                               864       A64
                                                               963       A82
                                                               A62       C62
                                                               C42       E42
                                                                         8642

Mathematica

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

Crossrefs

The non-strict case is A328187.

Partitions with all consecutive parts relatively prime are A328172, with strict case A328188.

Strict partitions with relatively prime parts are A078374.

Partitions with no consecutive divisibilities are A328171.

Cf. A000837, A018783, A070211, A289509, A318980, A325545, A328170, A328221, A328335, A328336.

Sequence in context: A303280 A318717 A331887 * A134192 A358344 A309342

Adjacent sequences: A328217 A328218 A328219 * A328221 A328222 A328223

Keyword

nonn

Author

Gus Wiseman, Oct 14 2019

Status

approved