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A109037
Number of irreducible partitions into triangular numbers. A partition is irreducible if no subpartition with 2 or more parts sums to a triangular number.
1
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 3, 3, 3, 1, 2, 3, 3, 3, 4, 2, 1, 2, 5, 4, 5, 5, 3, 4, 1, 3, 2, 3, 6, 5, 4, 5, 5, 1, 4, 6, 5, 4, 8, 5, 6, 9, 10, 1, 3, 5, 9, 9, 10, 9, 9, 10, 7, 6, 1, 4, 10, 9, 7, 11, 7, 8, 12, 14, 7, 11, 1, 9, 13, 9, 12, 9, 9, 15, 16, 12, 11, 16, 15, 1, 8, 11, 8, 16
OFFSET
0,13
COMMENTS
Sequence is almosot certainly unbounded. Obviously it contains infinitely many 1's, at triangular indices. At non-triangular 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.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved