cp's OEIS Frontend

A147583 Number of partitions of n into distinct parts such that 5*u<=v for all pairs (u,v) of parts with u

%I A147583 #9 Oct 10 2013 16:28:22
%S A147583 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 A147583 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 A147583 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 A147583 Number of partitions of n into distinct parts such that 5*u<=v for all pairs (u,v) of parts with u<v.
%C A147583 From _Edward Early_, Jan 10 2009: (Start)
%C A147583 Also the dimension of the n-th degree part of the mod 5 Steenrod algebra.
%C A147583 Also the number of partitions into parts (5^j-1)/4=1+5+5^2+...+5^(j-1) for j>=1. (End)
%H A147583 Reinhard Zumkeller, <a href="/A147583/b147583.txt">Table of n, a(n) for n = 1..1000</a>
%e A147583 a(29) = #{29,28+1,27+2,26+3,25+4} = 5;
%e A147583 a(30) = #{30,29+1,28+2,27+3,26+4,25+5} = 6;
%e A147583 a(31) = #{31,30+1,29+2,28+3,27+4,26+5,25+5+1} = 7.
%o A147583 (Haskell)
%o A147583 a147583 = p [1..] where
%o A147583    p _      0 = 1
%o A147583    p (k:ks) m = if m < k then 0 else p [5 * k ..] (m - k) + p ks m
%o A147583 -- _Reinhard Zumkeller_, Oct 10 2013
%Y A147583 Cf. A000041, A000009, A000929, A132011.
%K A147583 nonn
%O A147583 1,6
%A A147583 _Reinhard Zumkeller_, following a suggestion of Clark Hanley (clark.hanley(AT)gmx.com), Nov 08 2008