This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A274733 #15 Feb 16 2025 08:33:36 %S A274733 1,1,8,26,123,334,1295,3222,10172,25300,69258,161259,417582,925972, %T A274733 2200395,4794092,10769222,22543912,48728784,98926942 %N A274733 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 A274733 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 A274733 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 A274733 By numerical experimentation, it seems a(n) is the convolution of A000009 (with offset 1) and A260664. (conjectured) %H A274733 George Beck, <a href="/A274733/a274733.nb">triple intersections of partitions.nb</a> %H A274733 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 A274733 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentagonalNumberTheorem.html">Pentagonal Number Theorem</a> %H A274733 Wikipedia, <a href="http://www.wikipedia.org/wiki/Pentagonal_number_theorem">Pentagonal number theorem</a> %e A274733 For an example for double intersections, see A274521. %Y A274733 Cf. A000009, A260664, A274521. %K A274733 nonn,more %O A274733 1,3 %A A274733 _George Beck_, Jul 04 2016