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%I #19 Jul 04 2019 10:27:56
%S 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,
%T 130,208,191,286,267,402,368,546,518,730,709,998,954,1322,1305,1751,
%U 1740,2330,2299,3056,3074,3968,4031,5202,5249,6721,6877,8642,8888,11147,11432,14248,14747,18097,18838,23093,23938,29186,30489
%N Number of partitions of n where the minimal multiplicity of any part is 2.
%H Joerg Arndt and Alois P. Heinz, <a href="/A244515/b244515.txt">Table of n, a(n) for n = 1..1000</a>
%e From _Gus Wiseman_, Jul 03 2019: (Start)
%e 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.
%e 11 22 33 22111 44 33111 55 33311 66
%e 2211 3311 2211111 3322 44111 4422
%e 22211 4411 3311111 5511
%e 221111 222211 221111111 33222
%e 331111 332211
%e 22111111 441111
%e 2222211
%e 33111111
%e 2211111111
%e (End)
%p b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p b(n, i-1, k) +add(b(n-i*j, i-1, k), j=max(1, k)..n/i)))
%p end:
%p a:= n-> b(n$2, 2) -b(n$2, 3):
%p seq(a(n), n=1..80);
%t 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}]]];
%t a[n_] := b[n, n, 2] - b[n, n, 3];
%t Array[a, 80] (* _Jean-François Alcover_, May 01 2018, translated from Maple *)
%t Table[Length[Select[IntegerPartitions[n],Min@@Length/@Split[#]==2&]],{n,0,30}] (* _Gus Wiseman_, Jul 03 2019 *)
%Y Column k = 2 of A243978.
%Y Cf. A000041, A007690, A008284, A116608, A325240, A325242.
%K nonn
%O 1,6
%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 29 2014
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