A101268 - OEIS

A101268

Number of compositions of n into pairwise relatively prime parts.

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

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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.

Cf. A087087, A302569, A305713, A326675, A327516, A328673, A333227, A333228.

Sequence in context: A151897 A192758 A085489 * A188920 A281362 A319111

Adjacent sequences: A101265 A101266 A101267 * A101269 A101270 A101271

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Dec 18 2004

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Jun 14 2017

STATUS

approved