cp's OEIS Frontend

A326292 Number of crossing integer partitions of n.

%I A326292 #8 Jun 28 2020 02:48:02
%S A326292 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,
%T A326292 3,5,7,11,15,22,30,43,57,80,105,142,186,248,320,421,539,698,889,1140,
%U A326292 1438,1827,2291,2882,3593,4489,5559,6902,8503,10484,12853,15763
%N A326292 Number of crossing integer partitions of n.
%C A326292 A multiset partition is crossing if it has two blocks of the form {...x...y...}, {...z...t...} where x < z < y < t or z < x < t < y. An integer partition is crossing if, by replacing each part with its multiset of prime indices, we obtain a crossing multiset partition.
%e A326292 The a(31) = 1 through a(36) = 7 partitions:
%e A326292   21,10  21,10,1  21,10,2    21,10,3      21,10,4        21,10,5
%e A326292                   21,10,1,1  21,10,2,1    21,10,2,2      21,10,3,2
%e A326292                              21,10,1,1,1  21,10,3,1      21,10,4,1
%e A326292                                           21,10,2,1,1    21,10,2,2,1
%e A326292                                           21,10,1,1,1,1  21,10,3,1,1
%e A326292                                                          21,10,2,1,1,1
%e A326292                                                          21,10,1,1,1,1,1
%t A326292 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A326292 croXQ[stn_]:=MatchQ[stn,{___,{___,x_,___,y_,___},___,{___,z_,___,t_,___},___}/;x<z<y<t||z<x<t<y];
%t A326292 Table[Length[Select[IntegerPartitions[n],croXQ[primeMS/@#]&]],{n,0,40}]
%Y A326292 The Heinz numbers of these partitions are given by A324170.
%Y A326292 Cf. A000108, A002662, A016098, A056239, A112798, A324172, A324326, A326210, A326252, A326332.
%K A326292 nonn
%O A326292 0,34
%A A326292 _Gus Wiseman_, Oct 03 2019
%E A326292 More terms from _Jinyuan Wang_, Jun 28 2020