A330774 Number of n-color perfect compositions of n.

1, 1, 1, 5, 1, 11, 1, 61, 7, 15, 1, 259, 1, 19, 17, 1901, 1, 383, 1, 511, 21, 27, 1, 14147, 11, 31, 187, 859, 1, 1403, 1, 147661, 29, 39, 25, 39307, 1, 43, 33, 42351, 1, 2303, 1, 1843, 947, 51, 1, 1815811, 15, 1255, 41, 2479, 1, 46697, 33, 97339, 45, 63, 1, 219347, 1

Offset

0,4

Comments

An n-color perfect composition of v is a composition into j types of each part j whose sequence of parts contains one composition of every positive integer less than n.

Links

Table of n, a(n) for n=0..60.

A. O. Munagi, Perfect Compositions of Numbers, J. Integer Seq. 23 (2020), art. 20.5.1.

Example

a(5)=11 because v=5 has eleven n-color perfect compositions: (1,1,1,1,1), (1,2,2),(2,2,1), (1,2',2'), (2',2',1), (1,1,3), (3,1,1), (1,1,3'), (3',1,1), (1,1,3''), (3'',1,1).

Crossrefs

Cf. A330773, A165552, A001906, A002033, A074206.

Sequence in context: A245211 A356775 A347389 * A296307 A238554 A067292

Adjacent sequences: A330771 A330772 A330773 * A330775 A330776 A330777

Keyword

nonn

Author

Augustine O. Munagi, Dec 30 2019

Status

approved