A304871 - OEIS

%I #16 May 21 2018 09:55:06

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

%T 0,1,3,1,1,0,0,0,0,0,1,4,1,1,0,0,0,0,0,0,1,5,1,1,0,0,0,0,0,0,0,1,5,2,

%U 1,1,0,0,0,0,0,0,0,1,6,2,1,1,0,0,0,0,0,0,0,0,1

%N Triangle read by rows: T(n, k) gives the number of partitions (d1,d2,...,dm) of n such that k = d1/1 <= d2/2 <= ... <= dm/m for 1 <= k <= n.

%H Seiichi Manyama, <a href="/A304871/b304871.txt">Rows n = 1..100, flattened</a>

%e The partitions (d1,d2,...,dm) of 9 such that 1 = d1/1 <= d2/2 <= ... <= dm/m are (1, 8), (1, 2, 6) and (1, 3, 5). So T(9, 1) = 3.

%e First few rows are:

%e   1;

%e   0, 1;

%e   1, 0, 1;

%e   1, 0, 0, 1;

%e   1, 0, 0, 0, 1;

%e   2, 1, 0, 0, 0, 1;

%e   2, 1, 0, 0, 0, 0, 1;

%e   2, 1, 0, 0, 0, 0, 0, 1;

%e   3, 1, 1, 0, 0, 0, 0, 0, 1;

%e   4, 1, 1, 0, 0, 0, 0, 0, 0, 1;

%Y Row sums give A053282.

%Y Cf. A304869.

%K nonn,tabl

%O 1,16

%A _Seiichi Manyama_, May 20 2018