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A328220
Number of strict integer partitions of n with no pair of consecutive parts relatively prime.
13
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.
Sequence in context: A303280 A318717 A331887 * A134192 A358344 A309342
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 14 2019
STATUS
approved