A328220 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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