A228823 Triangle read by rows: T(n,k) = total number of parts in all partitions of n that contain k as a part, n>=1, 1<=k<=n.

1, 2, 1, 5, 2, 1, 9, 5, 2, 1, 17, 9, 5, 2, 1, 27, 17, 9, 5, 2, 1, 46, 27, 17, 9, 5, 2, 1, 69, 46, 27, 17, 9, 5, 2, 1, 108, 69, 46, 27, 17, 9, 5, 2, 1, 158, 108, 69, 46, 27, 17, 9, 5, 2, 1, 234, 158, 108, 69, 46, 27, 17, 9, 5, 2, 1, 331, 234, 158, 108, 69

Offset: 1

Author

Omar E. Pol, Sep 25 2013

Keywords

• nonn
• tabl

Comments

Row n lists the first n elements of A093694 in decreasing order.

Examples

			Triangle begins:
1;
2,     1;
5,     2,   1;
9,     5,   2,   1;
17,    9,   5,   2,  1;
27,   17,   9,   5,  2,  1;
46,   27,  17,   9,  5,  2,  1;
69,   46,  27,  17,  9,  5,  2,  1;
108,  69,  46,  27, 17,  9,  5,  2,  1;
158, 108,  69,  46, 27, 17,  9,  5,  2,  1;
234, 158, 108,  69, 46, 27, 17,  9,  5,  2,  1;
331, 234, 158, 108, 69, 46, 27, 17,  9,  5,  2,  1;
		

Crossrefs

Cf. A000041, A006128, A027293, A093694, A182701.

Formula

T(n,k) = A000041(n-k) + A006128(n-k) = A093694(n-k).