A027185 Triangular array O by rows: O(n,k) = number of partitions of n into an odd number of parts, the least being k.

1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 3, 0, 0, 0, 1, 3, 1, 0, 0, 0, 1, 6, 1, 0, 0, 0, 0, 1, 7, 2, 0, 0, 0, 0, 0, 1, 12, 2, 1, 0, 0, 0, 0, 0, 1, 14, 4, 1, 0, 0, 0, 0, 0, 0, 1, 22, 4, 2, 0, 0, 0, 0, 0, 0, 0, 1, 27, 6, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 40, 7, 3, 1, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• tabl

Examples

			1,
0, 1,
1, 0, 1,
1, 0, 0, 1,
3, 0, 0, 0, 1,
3, 1, 0, 0, 0, 1,
6, 1, 0, 0, 0, 0, 1,
7, 2, 0, 0, 0, 0, 0, 1,
12, 2, 1, 0, 0, 0, 0, 0, 1,
14, 4, 1, 0, 0, 0, 0, 0, 0, 1,
22, 4, 2, 0, 0, 0, 0, 0, 0, 0, 1,
27, 6, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1,
40, 7, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1,
		

Crossrefs

Cf. A027186.

Formula

O(n, k) = E(n-k, k)+E(n-k, k+1)+...+E(n-k, n-k), for 2<=2k<=n, E given by A027186.

T(n,k) + A027186(n,k) = A026794(n,k). - R. J. Mathar, Oct 18 2019