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A244516 Number of partitions of n where the minimal multiplicity of any part is 3. 2

%I #10 May 01 2018 02:47:12

%S 0,0,1,0,0,1,0,0,2,1,2,3,3,2,7,3,5,9,8,7,16,12,17,23,23,25,42,33,43,

%T 59,61,59,95,85,104,128,137,148,207,189,233,283,307,320,430,424,498,

%U 584,634,686,872,864,1011,1177,1280,1365,1687,1736,1987,2258,2470,2674,3208,3303,3767,4277,4658,5014,5916,6201

%N Number of partitions of n where the minimal multiplicity of any part is 3.

%C Column k=3 of A243978.

%H Joerg Arndt and Alois P. Heinz, <a href="/A244516/b244516.txt">Table of n, a(n) for n = 1..1000</a>

%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, 3) -b(n$2, 4):

%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, 3] - b[n, n, 4];

%t Array[a, 80] (* _Jean-Fran├žois Alcover_, May 01 2018, translated from Maple *)

%K nonn

%O 1,9

%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 29 2014

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Last modified March 3 00:46 EST 2024. Contains 370499 sequences. (Running on oeis4.)