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

1,2

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

Links

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

Example

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;

Crossrefs

Column 1 is A046746. Row sums give A066186.

Cf. A014153, A181187, A194714.

Sequence in context: A142048 A117563 A060439 * A135224 A209578 A268829

Adjacent sequences: A206280 A206281 A206282 * A206284 A206285 A206286

Keyword

nonn,tabl

Author

Omar E. Pol, Feb 13 2012

Extensions

More terms from Alois P. Heinz, Feb 13 2012

Status

approved