Search: id:A109035
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%I A109035
%S A109035 1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,2,2,3,2,2,2,1,2,2,3,2,3,2,3,3,2,
%T A109035 3,1,2,2,3,1,2,3,3,3,2,3,3,5,1,2,3,4,4,4,5,5,6,4,4,5,3,3,4,1,3,5,6,6,7,
%U A109035 7,7,6,6,3,5,7,8,7,8,7,1,4,5,9,5,5,6,10,4,6,9,11,11,10,10,11,8,7,6,1,7
%N A109035 Number of irreducible partitions into squares. A partition is irreducible 
               if no subpartition with 2 or more parts sums to a square.
%C A109035 Sequence is unbounded, as can be seen by considering sums of 2 squares 
               (thanks to David Harden). Obviously it contains infinitely many 1's, 
               at square indices. At non-square indices, series appears to go to 
               infinity, but this is conjecture and growth rate is entirely unknown. 
               Also unknown is whether the sequence is onto the positive integers.
%e A109035 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 A109035 Cf: A001156, A109036.
%Y A109035 Sequence in context: A025887 A025882 A025876 this_sequence A064823 A140225 
               A104758
%Y A109035 Adjacent sequences: A109032 A109033 A109034 this_sequence A109036 A109037 
               A109038
%K A109035 nonn
%O A109035 0,13
%A A109035 Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 16 2005

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