• A minimal operad
in the non-negative integers relative
to a given string *0, C*(*2*)*, …, C*(*k*)

is defined by extending the sequence:

*C*(*n*)* = *max{*C*(*i*)* + C*(*n-i*)}*i=1…n-1** *for * n > k.*

(minimal in
the sense that each term is no larger than needed.)

3) *C**0, 1** = 0, 1, 1, 2, 2, 3, 3, …*

4) *C**0, 1 ,1, 2, 3** = 0, 1, 1, 2, 3, 3, 4, 4, 5, 6, …*

5) *C**0, 0, 0,
0, 0, 1, 2, 3, 4, 5, 6**=0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6,
*

OPEN question: find a closed formula for these
sequences.

NOTE: The terms oscillate around linear growth.