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Table of distinct numbers of the form v*w + w*u + u*v with 1 <= u <= v <= w <= n.
5

%I #15 Dec 04 2013 06:50:59

%S 3,3,5,8,12,3,5,7,8,11,12,15,16,21,27,3,5,7,8,9,11,12,14,15,16,19,20,

%T 21,24,26,27,32,33,40,48,3,5,7,8,9,11,12,14,15,16,17,19,20,21,23,24,

%U 26,27,29,31,32,33,35,38,39,40,45,47,48,55,56,65,75,3,5

%N Table of distinct numbers of the form v*w + w*u + u*v with 1 <= u <= v <= w <= n.

%C A100440(n) = number of terms in row n;

%C T(1,1) = 3; right edge: T(n,A100440(n)) = A033428(n);

%C T(n,k) = T(n+1,k) for k <= A200742(n);

%C distinct terms per row of table in A200737.

%H Reinhard Zumkeller, <a href="/A200741/b200741.txt">Rows n=1..25 of triangle, flattened</a>

%t row[n_] := Table[v*w + w*u + u*v, {u, 1, n}, {v, u, n}, {w, v, n}] // Flatten // Union; Table[row[n], {n, 1, 6}] // Flatten (* _Jean-François Alcover_, Dec 04 2013 *)

%o (Haskell)

%o import Data.List (nub)

%o a200741 n k = a200741_tabl !! (n-1) !! (k-1)

%o a200741_row = nub . a200737_row

%o a200741_tabl = map a200741_row [1..]

%K nonn,tabf

%O 1,1

%A _Reinhard Zumkeller_, Nov 21 2011