A206283 Triangle read by rows: T(n,k) = sum of the k-th parts of all partitions of n with their parts written in nondecreasing order.

1, 3, 1, 5, 3, 1, 9, 7, 3, 1, 12, 12, 7, 3, 1, 20, 21, 14, 7, 3, 1, 25, 31, 24, 14, 7, 3, 1, 38, 47, 40, 26, 14, 7, 3, 1, 49, 66, 61, 43, 26, 14, 7, 3, 1, 69, 93, 92, 70, 45, 26, 14, 7, 3, 1, 87, 124, 130, 106, 73, 45, 26, 14, 7, 3, 1

Offset: 1

Author

Omar E. Pol, Feb 13 2012

Keywords

• nonn
• tabl

Comments

In row n, the sum of all odd-indexed terms minus the sum of all even-indexed terms is equal to A194714(n).

Reversed rows converge to A014153. - Alois P. Heinz, Feb 13 2012

Examples

			Row 4 is 9, 7, 3, 1 because the five partitions of 4, with their parts written in nondecreasing order, are
.                               4
.                               1, 3
.                               2, 2
.                               1, 1, 2
.                               1, 1, 1, 1
-------------------------------------------
And the sums of the columns are 9, 7, 3, 1.
.
Triangle begins:
   1;
   3,  1;
   5,  3,  1;
   9,  7,  3,  1;
  12, 12,  7,  3,  1;
  20, 21, 14,  7,  3,  1;
  25, 31, 24, 14,  7,  3,  1;
  38, 47, 40, 26, 14,  7,  3,  1;
  49, 66, 61, 43, 26, 14,  7,  3,  1;
  69, 93, 92, 70, 45, 26, 14,  7,  3,  1;
		

Links

• Alois P. Heinz, Rows n = 1..70, flattened

Crossrefs

Column 1 is A046746. Row sums give A066186.

Cf. A014153, A181187, A194714.

Extensions

More terms from Alois P. Heinz, Feb 13 2012