cp's OEIS Frontend

A236972 The number of partitions of n into at least 5 parts from which we can form every partition of n into 5 parts by summing elements.

%I A236972 #9 Mar 01 2014 21:15:54
%S A236972 0,0,0,0,1,2,2,3,3,4,7,8,9,13,14,24,29,35,38
%N A236972 The number of partitions of n into at least 5 parts from which we can form every partition of n into 5 parts by summing elements.
%C A236972 The corresponding partitions with 2 in the definition instead of 5 are the complete partitions, which A126796 counts.
%C A236972 The qualifier 'into at least 5 parts' is only relevant for n = 1, 2, 3 or 4. It is included because otherwise the condition would be vacuously true for all partitions of 1, 2, 3 and 4. It seems neater to consider that there are no partitions of 1, 2, 3 or 4 of this form.
%C A236972 What is the limit for large n of the proportion of partitions of n for which this holds, or this sequence divided by A000041?
%e A236972 The valid partitions of 11 are all those which contain only 1's, 2's and 3's, with no more than one 3 and no more than three 2's or 3's. This is because every partition of 11 into 5 parts contains at least one element 3 or more, and at least 3 elements 2 or more. There are 7 such partitions, therefore a(11) = 7.
%Y A236972 A000041 counts partitions, A126796 counts complete partitions - the case for partitions into 2 instead of 5, A236970 and A236971 are the cases for 3 and 4 respectively.
%K A236972 nonn,more
%O A236972 1,6
%A A236972 _Jack W Grahl_, Feb 02 2014