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A109038 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. 1
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,13

COMMENTS

Same as A109037 except at triangular indices. Conjecture than lim_{n->\inf} a(n) = \inf.

LINKS

Table of n, a(n) for n=0..94.

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

Cf: A007294, A109037.

Sequence in context: A165074 A273165 A095139 * A208246 A320857 A211664

Adjacent sequences:  A109035 A109036 A109037 * A109039 A109040 A109041

KEYWORD

nonn

AUTHOR

Franklin T. Adams-Watters, Jun 16 2005

STATUS

approved

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Last modified November 15 11:18 EST 2019. Contains 329144 sequences. (Running on oeis4.)