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 A209297 Triangle read by rows: T(n,k) = k*n + k - n, 1 <= k <= n. 10
 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 (list; table; graph; refs; listen; history; text; internal format)
 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) 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

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Last modified June 30 14:43 EDT 2022. Contains 354940 sequences. (Running on oeis4.)