A303942 - OEIS

%I #20 May 04 2018 11:05:07

%S 1,1,0,0,1,1,0,0,1,2,1,0,0,1,1,0,1,2,2,1,1,1,1,1,1,3,3,2,1,2,2,1,2,3,

%T 4,3,3,2,2,2,2,4,4,4,3,4,3,2,3,5,7,5,5,5,6,4,3,6,8,8,5,6,6,6,6,7,9,9,

%U 10,8,8,7,8,10,11,12,10,11,10,10,9,12,15,14,14

%N Number of partitions of n into at most 1 copy of 1^2, 2 copies of 2^2, 3 copies of 3^2, ... .

%H Seiichi Manyama, <a href="/A303942/b303942.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{k>=1} (1-x^(k^2*(k+1)))/(1-x^(k^2)).

%e    n |              | a(n)

%e -----+--------------+------

%e    1 | 1            |  1

%e    4 | 4            |  1

%e    5 | 4+1          |  1

%e    8 | 4+4          |  1

%e    9 | 9, 4+4+1     |  2

%e   10 | 9+1          |  1

%e   13 | 9+4          |  1

%e   14 | 9+4+1        |  1

%e   16 | 16           |  1

%e   17 | 16+1, 9+4+4  |  2

%e   18 | 9+9, 9+4+4+1 |  2

%Y Cf. A011379, A033461, A052335, A303944, A303947.

%K nonn,look

%O 0,10

%A _Seiichi Manyama_, May 03 2018