OFFSET
0,3
COMMENTS
If we form a multiorder by treating integer partitions (a,...,z) as multiarrows LCM(a,...,z) <= {z,...,a}, then a(n) is the number of triangles of weight n.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
EXAMPLE
The a(4) = 17 ordered multiset partitions:
{{4}} {{1,3}} {{2,2}} {{1,1,2}} {{1,1,1,1}}
{{1},{3}} {{2},{2}} {{1},{1,2}} {{1},{1,1,1}}
{{1,1},{2}} {{1,1,1},{1}}
{{1},{1},{2}} {{1,1},{1,1}}
{{1},{1},{1,1}}
{{1},{1,1},{1}}
{{1,1},{1},{1}}
{{1},{1},{1},{1}}
PROG
(PARI) seq(n)={my(M=Map()); for(m=1, n, forpart(p=m, my(k=lcm(Vec(p)), z); mapput(M, k, if(mapisdefined(M, k, &z), z, 1 + O(x*x^n)) - x^m))); Vec(1/vecprod(Mat(M)[, 2]))} \\ Andrew Howroyd, Jan 16 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 07 2018
EXTENSIONS
a(0)=1 prepended and terms a(11) and beyond from Andrew Howroyd, Jan 16 2023
STATUS
approved