OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..400
FORMULA
a(n) = 1 + Sum_{j=0..n} binomial(n*(n-j)+j,j) if n>1, a(0) = a(1) = 1.
EXAMPLE
a(0) = 1: the empty composition.
a(1) = 1: 1.
a(2) = 6: 1111, 112, 121, 211, 22, 4.
a(3) = 20: 111111111, 1111113, 1111131, 1111311, 1113111, 1131111, 1311111, 3111111, 11133, 11313, 11331, 13113, 13131, 13311, 31113, 31131, 31311, 33111, 333, 9.
MAPLE
a:= n-> `if`(n<2, 1, 1+add(binomial(n*(n-j)+j, j), j=0..n)):
seq(a(n), n=0..21);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 06 2020
STATUS
approved