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%I #14 Aug 25 2020 06:35:15
%S 1,1,8,26,123,334,1295,3222,10172,25300,69258,161259,417582,925972,
%T 2200395,4794092,10769222,22543912,48728784,98926942
%N 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.
%C Let a(n) be the number of odd partitions in the multiset intersections of the set of partitions of n with itself three times.
%C 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".)
%C By numerical experimentation, it seems a(n) is the convolution of A000009 (with offset 1) and A260664. (conjectured)
%H George Beck, <a href="/A274733/a274733.nb">triple intersections of partitions.nb</a>
%H Sylvie Corteel, Carla D. Savage, Herbert S. Wilf, Doron Zeilberger, <a href="http://dx.doi.org/10.1006/jcta.1997.2846">A pentagonal number sieve</a>, J. Combin. Theory Ser. A 82 (1998), no. 2, 186-192.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PentagonalNumberTheorem.html">Pentagonal Number Theorem</a>
%H Wikipedia, <a href="http://www.wikipedia.org/wiki/Pentagonal_number_theorem">Pentagonal number theorem</a>
%e For an example for double intersections, see A274521.
%Y Cf. A000009, A260664, A274521.
%K nonn,more
%O 1,3
%A _George Beck_, Jul 04 2016
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