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

1,3

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)

Links

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

Formula

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

Example

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)

Mathematica

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

Prog

(Haskell)
a209297 n k = k * n + k - n
a209297_row n = map (a209297 n) [1..n]
a209297_tabl = map a209297_row [1..]
(GAP) Flat(List([1..10^3], n -> List([1..n], k -> k * n + k - n))); # Muniru A Asiru, Oct 31 2017

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).

Sequence in context: A016687 A139356 A318359 * A243525 A300071 A155060

Adjacent sequences: A209294 A209295 A209296 * A209298 A209299 A209300

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Jan 19 2013

Status

approved