OFFSET
0,3
FORMULA
Weigh transform of A089259. The weigh transform of a sequence (s_1, s_2, ...) is the sequence with generating function Product_{i > 0} (1 + x^i)^s_i.
EXAMPLE
The a(4) = 12 partitions:
((4)) ((2)(2)) ((13)) ((1)(12)) ((1)(1)(1)(1))
((1)(3)) ((1)(1)(2)) ((1))((1)(1)(1))
((1))((3)) ((1))((12))
((1))((1)(2))
((2))((1)(1))
MATHEMATICA
ppl[n_, k_]:=Switch[k, 0, {n}, 1, IntegerPartitions[n], _, Join@@Table[Union[Sort/@Tuples[ppl[#, k-1]&/@ptn]], {ptn, IntegerPartitions[n]}]];
Table[Length[Select[ppl[n, 3], And[UnsameQ@@#, And@@UnsameQ@@@Join@@#]&]], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 17 2019
STATUS
approved