OFFSET
0,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
Gus Wiseman, The a(5) = 25 split partitions.
Gus Wiseman, The a(6) = 52 split partitions.
EXAMPLE
The a(4) = 14 split partitions:
(4)
(31)
(22)
(211)
(3)(1)
(2)(2)
(1111)
(21)(1)
(2)(11)
(111)(1)
(11)(11)
(2)(1)(1)
(11)(1)(1)
(1)(1)(1)(1)
MATHEMATICA
comps[q_]:=Table[Table[Take[q, {Total[Take[c, i-1]]+1, Total[Take[c, i]]}], {i, Length[c]}], {c, Join@@Permutations/@IntegerPartitions[Length[q]]}];
Table[Sum[Length[Select[comps[y], OrderedQ[Total/@#, GreaterEqual]&]], {y, IntegerPartitions[n]}], {n, 10}]
PROG
(PARI) a(n)={my(recurse(r, m, s, t, f)=if(m==0, r==0, if(f, self()(r, min(m, t), t, 0, 0)) + self()(r, m-1, s, t, 0) + if(t+m<=s, self()(r-m, min(m, r-m), s, t+m, 1)))); recurse(n, n, n, 0, 0)} \\ Andrew Howroyd, Jan 18 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 29 2018
EXTENSIONS
a(21) onwards from Andrew Howroyd, Jan 18 2024
STATUS
approved