|
|
A244515
|
|
Number of partitions of n where the minimal multiplicity of any part is 2.
|
|
5
|
|
|
0, 1, 0, 1, 0, 2, 1, 4, 2, 6, 4, 9, 6, 16, 9, 23, 18, 34, 27, 51, 40, 75, 63, 103, 90, 152, 130, 208, 191, 286, 267, 402, 368, 546, 518, 730, 709, 998, 954, 1322, 1305, 1751, 1740, 2330, 2299, 3056, 3074, 3968, 4031, 5202, 5249, 6721, 6877, 8642, 8888, 11147, 11432, 14248, 14747, 18097, 18838, 23093, 23938, 29186, 30489
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,6
|
|
LINKS
|
|
|
EXAMPLE
|
The a(2) = 1 through a(12) = 9 partitions are the following (empty columns not shown). The Heinz numbers of these partitions are given by A325240.
11 22 33 22111 44 33111 55 33311 66
2211 3311 2211111 3322 44111 4422
22211 4411 3311111 5511
221111 222211 221111111 33222
331111 332211
22111111 441111
2222211
33111111
2211111111
(End)
|
|
MAPLE
|
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1, k) +add(b(n-i*j, i-1, k), j=max(1, k)..n/i)))
end:
a:= n-> b(n$2, 2) -b(n$2, 3):
seq(a(n), n=1..80);
|
|
MATHEMATICA
|
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k] + Sum[b[n - i*j, i - 1, k], {j, Max[1, k], n/i}]]];
a[n_] := b[n, n, 2] - b[n, n, 3];
Table[Length[Select[IntegerPartitions[n], Min@@Length/@Split[#]==2&]], {n, 0, 30}] (* Gus Wiseman, Jul 03 2019 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|