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A337600
Number of unordered triples of positive integers summing to n whose set of distinct parts is pairwise coprime, where a singleton is always considered coprime.
10
0, 0, 0, 1, 1, 2, 3, 3, 4, 5, 5, 6, 9, 7, 10, 8, 11, 11, 18, 12, 19, 13, 19, 17, 30, 16, 28, 20, 31, 23, 47, 23, 42, 26, 45, 27, 60, 31, 57, 35, 61, 37, 85, 38, 75, 43, 74, 47, 108, 45, 98, 52, 96, 56, 136, 54, 115, 64, 117, 67, 175, 65, 139, 76, 144, 75, 195
OFFSET
0,6
COMMENTS
First differs from A337601 at a(9) = 5, A337601(9) = 4.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..10000
FORMULA
For n > 0, a(n) = A337601(n) + A079978(n).
EXAMPLE
The a(3) = 1 through a(14) = 10 partitions (A = 10, B = 11, C = 12):
111 211 221 222 322 332 333 433 443 444 544 554
311 321 331 431 441 532 533 543 553 743
411 511 521 522 541 551 552 661 752
611 531 721 722 651 733 761
711 811 731 732 751 833
911 741 922 851
831 B11 941
921 A31
A11 B21
C11
MATHEMATICA
Table[Length[Select[IntegerPartitions[n, {3}], SameQ@@#||CoprimeQ@@Union[#]&]], {n, 0, 100}]
CROSSREFS
A220377 is the strict case.
A304712 counts these partitions of any length.
A307719 is the strict case except for any number of 1's.
A337601 does not consider a singleton to be coprime unless it is (1).
A337602 is the ordered version.
A337664 counts compositions of this type and any length.
A000217 counts 3-part compositions.
A000837 counts relatively prime partitions.
A001399/A069905/A211540 count 3-part partitions.
A023023 counts relatively prime 3-part partitions.
A051424 counts pairwise coprime or singleton partitions.
A101268 counts pairwise coprime or singleton compositions.
A304709 counts partitions whose distinct parts are pairwise coprime.
A305713 counts pairwise coprime strict partitions.
A327516 counts pairwise coprime partitions.
A333227 ranks pairwise coprime compositions.
A333228 ranks compositions whose distinct parts are pairwise coprime.
A337461 counts pairwise coprime length-3 compositions.
A337563 counts pairwise coprime length-3 partitions with no 1's.
Sequence in context: A127039 A143091 A114539 * A238746 A272611 A156562
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 20 2020
STATUS
approved