A132015 Number of partitions of n into distinct parts such that u^2 < v for all pairs (u,v) of parts with u<v.

1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 18, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 22, 23, 24, 24, 24, 24, 24

Offset

1,3

Comments

A132016, A132017 and A132042 give record values and where and how often they occur.

Links

R. Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = f(n,1) with f(m,p) = if p=m then 1 else (if p<m then f(m-1,1+p^2)+f(m,p+1) else 0)."

Example

a(10) = #{10, 9+1, 8+2, 7+2+1} = 4;
a(11) = #{11, 10+1, 9+2, 8+2+1} = 4;
a(12) = #{12, 11+1, 10+2, 9+2+1} = 4;
a(13) = #{13, 12+1, 11+2, 10+3, 10+2+1} = 5;
a(14) = #{14, 13+1, 12+2, 11+3, 11+2+1, 10+3+1} = 6;
a(15) = #{15, 14+1, 13+2, 12+3, 12+2+1, 11+3+1} = 6.

Crossrefs

Cf. A000009, A132011.

Cf. A132085.

Sequence in context: A072613 A029551 A171482 * A120501 A113757 A291270

Adjacent sequences: A132012 A132013 A132014 * A132016 A132017 A132018

Keyword

nonn

Author

Reinhard Zumkeller, Aug 08 2007

Status

approved