A364526 Number of compositions (ordered partitions) of n into parts not greater than sqrt(n).

1, 1, 1, 1, 5, 8, 13, 21, 34, 149, 274, 504, 927, 1705, 3136, 5768, 20569, 39648, 76424, 147312, 283953, 547337, 1055026, 2033628, 3919944, 11749641, 23099186, 45411804, 89277256, 175514464, 345052351, 678355061, 1333610936, 2621810068, 5154342880, 10133171296

Offset: 0

Author

Ilya Gutkovskiy, Dec 22 2023

Keywords

• nonn

Links

• Index entries for sequences related to compositions

Crossrefs

Cf. A011782, A097356.

Programs

PARI

a(n)=my(s=sqrtint(n), x='x+O('x^(n+1))); polcoef(Pol(Ser(1/(1-sum(j=1,s,x^j)))),n);
vector(33,n,a(n-1)) \\ Joerg Arndt, Dec 22 2023

Formula

a(n) = [x^n] 1 / (1 - Sum_{1 <= j <= sqrt(n)} x^j).