A274534 Irregular triangle read by rows: T(n,k) = total number of k's in the first n antidiagonals of infinite Sudoku-type array A269526.

1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 3, 3, 2, 3, 2, 2, 3, 4, 3, 3, 3, 3, 1, 1, 4, 4, 4, 3, 4, 3, 2, 2, 1, 1, 5, 4, 4, 4, 5, 4, 3, 3, 2, 1, 1, 5, 5, 4, 5, 6, 5, 4, 4, 3, 1, 1, 1, 1, 5, 5, 5, 6, 7, 6, 5, 5, 4, 2, 2, 1, 1, 1, 5, 5, 6, 6, 7, 7, 6, 6, 5, 3, 3, 2, 1, 2, 1, 1, 5, 5, 6, 7, 7, 7, 7, 6, 6, 4, 4, 3, 2, 3, 2, 2, 1, 1

Offset: 1

Author

Omar E. Pol, Jun 30 2016

Keywords

• nonn
• look
• tabf

Comments

T(n,k) is also the total number of (k-1)'s in the first n antidiagonals of the square array A274528.

Examples

			Triangle begins:
1;
1, 1, 1;
1, 2, 2, 1;
2, 2, 2, 2, 1, 1;
3, 3, 2, 3, 2, 2;
3, 4, 3, 3, 3, 3, 1, 1;
4, 4, 4, 3, 4, 3, 2, 2, 1, 1;
5, 4, 4, 4, 5, 4, 3, 3, 2, 1, 1;
5, 5, 4, 5, 6, 5, 4, 4, 3, 1, 1, 1, 1;
5, 5, 5, 6, 7, 6, 5, 5, 4, 2, 2, 1, 1, 1;
5, 5, 6, 6, 7, 7, 6, 6, 5, 3, 3, 2, 1, 2, 1, 1;
5, 5, 6, 7, 7, 7, 7, 6, 6, 4, 4, 3, 2, 3, 2, 2, 1, 1;
5, 5, 7, 8, 7, 8, 8, 7, 7, 5, 5, 4, 3, 4, 3, 3, 1, 1;
...
For n = 3, the first three antidiagonals of the square array A269526 are [1], [3, 2], [2, 4, 3]. There are only one 1, two 2's, two 3's and only one 4, so the third row of the triangle is [1, 2, 2, 1].
		

Links

• Alois P. Heinz, Rows n = 1..175, flattened

Crossrefs

Cf. A269526, A274528.

Row sums give A000217, n >= 1.

Row lengths give A274529.