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%I #4 Mar 31 2012 13:21:29
%S 1,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,2,2,3,3,3,4,2,3,2,5,4,5,5,
%T 3,4,4,3,2,3,6,5,4,5,5,7,4,6,5,4,8,5,6,9,10,4,3,5,9,9,10,9,9,10,7,6,7,
%U 4,10,9,7,11,7,8,12,14,7,11,12,9,13,9,12,9,9,15,16,12,11,16,15,11,8,11,8
%N Number of irreducible partitions into smaller triangular numbers. A partition is irreducible if no subpartition with 2 or more parts sums to a smaller triangular number.
%C Same as A109037 except at triangular indices. Conjecture than lim_{n->\inf} a(n) = \inf.
%e a(9)=1 for the partition [6,3]. [6,1^3], [3^3], [3^2,1^3], [3,1^6] and [1^9] are all excluded because they contain subpartitions [3^2] or [1^3] summing to a triangular number.
%Y Cf: A007294, A109037.
%K nonn
%O 0,13
%A _Franklin T. Adams-Watters_, Jun 16 2005
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