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

%I A209297 #26 Feb 08 2024 09:48:39
%S A209297 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,
%T A209297 49,1,10,19,28,37,46,55,64,1,11,21,31,41,51,61,71,81,1,12,23,34,45,56,
%U A209297 67,78,89,100,1,13,25,37,49,61,73,85,97,109,121,1,14,27
%N A209297 Triangle read by rows: T(n,k) = k*n + k - n, 1 <= k <= n.
%C A209297 From _Michel Marcus_, May 18 2021: (Start)
%C A209297 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.
%C A209297                                              [1   2  3  4  5]
%C A209297                              [1   2  3  4]   [6   7  8  9 10]
%C A209297                    [1 2 3]   [5   6  7  8]   [11 12 13 14 15]
%C A209297           [1 2]    [4 5 6]   [9  10 11 12]   [16 17 18 19 20]
%C A209297   [1]     [3 4]    [7 8 9]   [13 14 15 16]   [21 22 23 24 25]
%C A209297   -----------------------------------------------------------
%C A209297    1       1 4      1 5 9     1  6  11 16     1  7  13 19 25
%C A209297 (End)
%H A209297 Reinhard Zumkeller, <a href="/A209297/b209297.txt">Rows n = 1..120 of triangle, flattened</a>
%F A209297 T(n,k) = (k-1)*(n+1)+1.
%e A209297 From _Muniru A Asiru_, Oct 31 2017: (Start)
%e A209297 Triangle begins:
%e A209297   1;
%e A209297   1,  4;
%e A209297   1,  5,  9;
%e A209297   1,  6, 11, 16;
%e A209297   1,  7, 13, 19, 25;
%e A209297   1,  8, 15, 22, 29, 36;
%e A209297   1,  9, 17, 25, 33, 41, 49;
%e A209297   1, 10, 19, 28, 37, 46, 55, 64;
%e A209297   1, 11, 21, 31, 41, 51, 61, 71, 81;
%e A209297   1, 12, 23, 34, 45, 56, 67, 78, 89, 100;
%e A209297   ... (End)
%t A209297 Array[Range[1, #^2, #+1]&,10] (* _Paolo Xausa_, Feb 08 2024 *)
%o A209297 (Haskell)
%o A209297 a209297 n k = k * n + k - n
%o A209297 a209297_row n = map (a209297 n) [1..n]
%o A209297 a209297_tabl = map a209297_row [1..]
%o A209297 (GAP) Flat(List([1..10^3], n -> List([1..n], k -> k * n + k - n))); # _Muniru A Asiru_, Oct 31 2017
%Y A209297 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).
%K A209297 nonn,tabl
%O A209297 1,3
%A A209297 _Reinhard Zumkeller_, Jan 19 2013