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A274733
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Number of odd partitions in the multiset of intersections of the set of partitions of n with itself three times; also number of distinct partitions in that multiset.
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1
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1, 1, 8, 26, 123, 334, 1295, 3222, 10172, 25300, 69258, 161259, 417582, 925972, 2200395, 4794092, 10769222, 22543912, 48728784, 98926942
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OFFSET
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1,3
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COMMENTS
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Let a(n) be the number of odd partitions in the multiset intersections of the set of partitions of n with itself three times.
Form the p(n) x p(n) x p(n) matrix M of partitions of numbers ranging from 1 to n by taking the multiset intersections of all the triples of partitions of n. Then, ignoring the empty set, the number of odd partitions in M equals the number of distinct partitions in M. (Proved in Wilf et al., "A pentagonal number sieve".)
By numerical experimentation, it seems a(n) is the convolution of A000009 (with offset 1) and A260664. (conjectured)
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LINKS
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Sylvie Corteel, Carla D. Savage, Herbert S. Wilf, Doron Zeilberger, A pentagonal number sieve, J. Combin. Theory Ser. A 82 (1998), no. 2, 186-192.
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EXAMPLE
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For an example for double intersections, see A274521.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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