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A328187
Number of integer partitions of n with no pair of consecutive parts relatively prime.
20
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.
Sequence in context: A339619 A018783 A200976 * A331885 A298971 A328602
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 12 2019
STATUS
approved