|
%I #15 Jan 29 2014 07:50:38
%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 21,24,26,27,32,33,40,48,3,5,7,8,9,11,11,12,14,15,16,17,19,20,21,23,
%U 24,24,26,27,29,31,32,33,35,38,39,40,45,47,48,55,56,65
%N Table of numbers of the form v*w + w*u + u*v with 1 <= u <= v <= w <= n, with repetitions.
%C A000292(n) = number of terms in row n;
%C T(1,1) = 3; right edge: T(n,A000292(n)) = A033428(n);
%C T(n,k) = T(n+1,k) for k <= A200738(n);
%C see table A200741 for distinct terms per row.
%H Reinhard Zumkeller, <a href="/A200737/b200737.txt">Rows n=1..25 of triangle, flattened</a>
%e First 5 rows:
%e 1: 3;
%e 2: 3,5,8,12;
%e 3: 3,5,7,8,11,12,15,16,21,27;
%e 4: 3,5,7,8,9,11,12,14,15,16,19,20,21,24,26,27,32,33,40,48;
%e 5: 3,5,7,8,9,11,11,12,14,15,16,17,19,20,21,23,24,24,26,27,29,31,... .
%e First terms of 5th row:
%e T(5,1) = 1*1 + 1*1 + 1*1 = 3;
%e T(5,2) = 1*2 + 2*1 + 1*1 = 5;
%e T(5,3) = 1*3 + 3*1 + 1*1 = 7;
%e T(5,4) = 2*2 + 2*1 + 1*2 = 8;
%e T(5,5) = 1*4 + 4*1 + 1*1 = 9;
%e T(5,6) = 1*5 + 5*1 + 1*1 = 11;
%e T(5,7) = 2*3 + 3*1 + 1*2 = 11 = T(5,6);
%e T(5,8) = 2*2 + 2*2 + 2*2 = 12;
%e T(5,9) = 2*4 + 4*1 + 1*2 = 14;
%e T(5,10) = 3*3 + 3*1 + 1*3 = 15;
%e T(5,11) = 2*3 + 3*2 + 2*2 = 16;
%e T(5,12) = 2*5 + 5*1 + 1*2 = 17; ... .
%o (Haskell)
%o import Data.List (sort)
%o a200737 n k = a200737_tabl !! (n-1) !! (k-1)
%o a200737_row n = sort
%o [v*w + w*u + u*v | w <- [1..n], v <- [1..w], u <- [1..v]]
%o a200737_tabl = map a200737_row [1..]
%K nonn,tabf,look
%O 1,1
%A _Reinhard Zumkeller_, Nov 21 2011
|
