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A385866 Triangle read by rows where T(n,k), for 1 <= k < n, is the row number where (n-k)^2 occurs in an n X n grid filled rowwise with the numbers 1 to n^2.

%I A385866 #34 Jul 17 2025 09:43:09
%S A385866 1,2,1,3,1,1,4,2,1,1,5,3,2,1,1,6,4,3,2,1,1,7,5,4,2,2,1,1,8,6,4,3,2,1,
%T A385866 1,1,9,7,5,4,3,2,1,1,1,10,8,6,5,4,3,2,1,1,1,11,9,7,6,5,3,3,2,1,1,1,12,
%U A385866 10,8,7,5,4,3,2,2,1,1,1,13,11,9,8,6,5,4,3,2,2,1,1,1
%N A385866 Triangle read by rows where T(n,k), for 1 <= k < n, is the row number where (n-k)^2 occurs in an n X n grid filled rowwise with the numbers 1 to n^2.
%C A385866 Rows are numbered starting from 1.
%F A385866 T(n, k) = floor(((n-k)^2 - 1) / n) + 1.
%e A385866       k=1  2  3  4  5  6
%e A385866   n=2:  1
%e A385866   n=3:  2, 1
%e A385866   n=4:  3, 1, 1
%e A385866   n=5:  4, 2, 1, 1
%e A385866   n=6:  5, 3, 2, 1, 1
%e A385866   n=7:  6, 4, 2, 2, 1, 1
%e A385866 For n = 5, the grid is:
%e A385866   1  2  3  4  5
%e A385866   6  7  8  9 10
%e A385866  11 12 13 14 15
%e A385866  16 17 18 19 20
%e A385866  21 22 23 24 25
%e A385866 The squares (n-k)^2 = {16, 9, 4, 1} are in row numbers {4, 2, 1, 1} respectively.
%t A385866 T[n_,k_]:=Floor[((n-k)^2-1)/n]+1;Table[T[n,k],{n,14},{k,n-1}]//Flatten (* _James C. McMahon_, Jul 17 2025 *)
%Y A385866 Cf. A385865 (column position).
%K A385866 nonn,easy,tabl
%O A385866 2,2
%A A385866 _Binay Krishna Maity_, Jul 10 2025