A132015
Number of partitions of n into distinct parts such that u^2 < v for all pairs (u,v) of parts with u
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
Keywords
Examples
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.
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
A147583
Number of partitions of n into distinct parts such that 5*u<=v for all pairs (u,v) of parts with u
1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 7, 7, 7, 7, 7, 8, 9, 9, 9, 9, 9, 10, 11, 11, 11, 11, 11, 12, 13, 13, 13, 13, 13, 14, 15, 15, 15, 15, 15, 16, 17, 18, 18, 18, 18, 19, 20, 21, 21, 21, 21, 22, 23, 24, 24, 24, 24, 25, 26, 27, 27, 27, 27
Offset: 1
Keywords
Comments
From Edward Early, Jan 10 2009: (Start)
Also the dimension of the n-th degree part of the mod 5 Steenrod algebra.
Also the number of partitions into parts (5^j-1)/4=1+5+5^2+...+5^(j-1) for j>=1. (End)
Examples
a(29) = #{29,28+1,27+2,26+3,25+4} = 5;
a(30) = #{30,29+1,28+2,27+3,26+4,25+5} = 6;
a(31) = #{31,30+1,29+2,28+3,27+4,26+5,25+5+1} = 7.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Programs
-
Haskell
a147583 = p [1..] where p _ 0 = 1 p (k:ks) m = if m < k then 0 else p [5 * k ..] (m - k) + p ks m -- Reinhard Zumkeller, Oct 10 2013
Comments