A147583 - OEIS

%I #9 Oct 10 2013 16:28:22

%S 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,

%T 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,

%U 16,17,18,18,18,18,19,20,21,21,21,21,22,23,24,24,24,24,25,26,27,27,27,27

%N Number of partitions of n into distinct parts such that 5*u<=v for all pairs (u,v) of parts with u<v.

%C From _Edward Early_, Jan 10 2009: (Start)

%C Also the dimension of the n-th degree part of the mod 5 Steenrod algebra.

%C Also the number of partitions into parts (5^j-1)/4=1+5+5^2+...+5^(j-1) for j>=1. (End)

%H Reinhard Zumkeller, <a href="/A147583/b147583.txt">Table of n, a(n) for n = 1..1000</a>

%e a(29) = #{29,28+1,27+2,26+3,25+4} = 5;

%e a(30) = #{30,29+1,28+2,27+3,26+4,25+5} = 6;

%e a(31) = #{31,30+1,29+2,28+3,27+4,26+5,25+5+1} = 7.

%o (Haskell)

%o a147583 = p [1..] where

%o    p _      0 = 1

%o    p (k:ks) m = if m < k then 0 else p [5 * k ..] (m - k) + p ks m

%o -- _Reinhard Zumkeller_, Oct 10 2013

%Y Cf. A000041, A000009, A000929, A132011.

%K nonn

%O 1,6

%A _Reinhard Zumkeller_, following a suggestion of Clark Hanley (clark.hanley(AT)gmx.com), Nov 08 2008