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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
Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 1..1000
EXAMPLE
From Gus Wiseman, Jul 03 2019: (Start)
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];
Array[a, 80] (* Jean-François Alcover, May 01 2018, translated from Maple *)
Table[Length[Select[IntegerPartitions[n], Min@@Length/@Split[#]==2&]], {n, 0, 30}] (* Gus Wiseman, Jul 03 2019 *)
CROSSREFS
Column k = 2 of A243978.
Sequence in context: A340621 A008733 A359907 * A154280 A004795 A161268
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jun 29 2014
STATUS
approved

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Last modified February 28 21:38 EST 2024. Contains 370400 sequences. (Running on oeis4.)