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

1,6

Comments

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

Links

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

Example

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].

Crossrefs

Cf. A269526, A274528.

Row sums give A000217, n >= 1.

Row lengths give A274529.

Sequence in context: A291592 A159905 A283735 * A224030 A233136 A339717

Adjacent sequences: A274531 A274532 A274533 * A274535 A274536 A274537

Keyword

nonn,look,tabf

Author

Omar E. Pol, Jun 30 2016

Status

approved