A209297 Triangle read by rows: T(n,k) = k*n + k - n, 1 <= k <= n.

1, 1, 4, 1, 5, 9, 1, 6, 11, 16, 1, 7, 13, 19, 25, 1, 8, 15, 22, 29, 36, 1, 9, 17, 25, 33, 41, 49, 1, 10, 19, 28, 37, 46, 55, 64, 1, 11, 21, 31, 41, 51, 61, 71, 81, 1, 12, 23, 34, 45, 56, 67, 78, 89, 100, 1, 13, 25, 37, 49, 61, 73, 85, 97, 109, 121, 1, 14, 27

Offset: 1

Author

Reinhard Zumkeller, Jan 19 2013

Keywords

• nonn
• tabl

Comments

From Michel Marcus, May 18 2021: (Start)

The n-th row of the triangle is the main diagonal of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows.

[1 2 3 4 5]

[1 2 3 4] [6 7 8 9 10]

[1 2 3] [5 6 7 8] [11 12 13 14 15]

[1 2] [4 5 6] [9 10 11 12] [16 17 18 19 20]

[1] [3 4] [7 8 9] [13 14 15 16] [21 22 23 24 25]

-----------------------------------------------------------

1 1 4 1 5 9 1 6 11 16 1 7 13 19 25

(End)

Examples

			From _Muniru A Asiru_, Oct 31 2017: (Start)
Triangle begins:
  1;
  1,  4;
  1,  5,  9;
  1,  6, 11, 16;
  1,  7, 13, 19, 25;
  1,  8, 15, 22, 29, 36;
  1,  9, 17, 25, 33, 41, 49;
  1, 10, 19, 28, 37, 46, 55, 64;
  1, 11, 21, 31, 41, 51, 61, 71, 81;
  1, 12, 23, 34, 45, 56, 67, 78, 89, 100;
  ... (End)
		

Links

• Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened

Crossrefs

Cf. A162610; A000012 (left edge), A000290 (right edge), A006003 (row sums), A001844 (central terms), A026741 (number of odd terms per row), A142150 (number of even terms per row), A221490 (number of primes per row).

Programs

GAP

Flat(List([1..10^3], n -> List([1..n], k -> k * n + k - n))); # Muniru A Asiru, Oct 31 2017

Haskell

a209297 n k = k * n + k - n
a209297_row n = map (a209297 n) [1..n]
a209297_tabl = map a209297_row [1..]

Mathematica

Array[Range[1, #^2, #+1]&,10] (* Paolo Xausa, Feb 08 2024 *)

Formula

T(n,k) = (k-1)*(n+1)+1.