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