A109036 - OEIS

%I #3 Mar 31 2012 13:21:29

%S 1,0,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,2,2,2,2,3,2,2,2,1,2,2,3,2,3,2,3,3,

%T 2,3,3,2,2,3,1,2,3,3,3,2,3,3,5,3,2,3,4,4,4,5,5,6,4,4,5,3,3,4,7,3,5,6,

%U 6,7,7,7,6,6,3,5,7,8,7,8,7,9,4,5,9,5,5,6,10,4,6,9,11,11,10,10,11,8,7,6,7,7

%N Number of irreducible partitions into smaller squares. A partition is irreducible if no subpartition with 2 or more parts sums to a square smaller than n.

%C This is the same as A109035 except for the values at squares. Conjecture that lim_{n->\inf} a(n) = \inf.

%e a(10)=1 for the partition [9,1]. [4^2,1^2], [4,1^6] and [1^10] are all excluded because they contain subpartitions [4^2,1] or [1^4] summing to a square.

%Y Cf: A109035, A001156.

%K nonn

%O 0,13

%A _Franklin T. Adams-Watters_, Jun 16 2005