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A101268 Number of compositions of n into pairwise relatively prime parts. 54
1, 1, 2, 4, 7, 13, 22, 38, 63, 101, 160, 254, 403, 635, 984, 1492, 2225, 3281, 4814, 7044, 10271, 14889, 21416, 30586, 43401, 61205, 85748, 119296, 164835, 226423, 309664, 422302, 574827, 781237, 1060182, 1436368, 1942589, 2622079, 3531152, 4742316, 6348411 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Here a singleton is always considered pairwise relatively prime. Compare to A337462. - Gus Wiseman, Oct 18 2020
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..500 (terms 0..400 from Alois P. Heinz)
Temba Shonhiwa, Compositions with pairwise relatively prime summands within a restricted setting, Fibonacci Quart. 44 (2006), no. 4, 316-323.
FORMULA
It seems that no formula is known.
EXAMPLE
From Gus Wiseman, Oct 18 2020: (Start)
The a(1) = 1 through a(5) = 13 compositions:
(1) (2) (3) (4) (5)
(11) (12) (13) (14)
(21) (31) (23)
(111) (112) (32)
(121) (41)
(211) (113)
(1111) (131)
(311)
(1112)
(1121)
(1211)
(2111)
(11111)
(End)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], Length[#]<=1||CoprimeQ@@#&]], {n, 0, 10}] (* Gus Wiseman, Oct 18 2020 *)
CROSSREFS
Row sums of A282748.
A051424 is the unordered version, with strict case A007360.
A335235 ranks these compositions.
A337461 counts these compositions of length 3, with unordered version A307719 and unordered strict version A220377.
A337462 does not consider a singleton to be coprime unless it is (1), with strict version A337561.
A337562 is the strict case.
A337664 looks only at distinct parts, with non-constant version A337665.
A000740 counts relatively prime compositions, with strict case A332004.
A178472 counts compositions with a common factor.
Sequence in context: A151897 A192758 A085489 * A188920 A281362 A319111
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Dec 18 2004
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Jun 14 2017
STATUS
approved

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Last modified March 18 22:22 EDT 2024. Contains 370951 sequences. (Running on oeis4.)