A200737 Table of numbers of the form v*w + w*u + u*v with 1 <= u <= v <= w <= n, with repetitions.

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, 21, 24, 26, 27, 32, 33, 40, 48, 3, 5, 7, 8, 9, 11, 11, 12, 14, 15, 16, 17, 19, 20, 21, 23, 24, 24, 26, 27, 29, 31, 32, 33, 35, 38, 39, 40, 45, 47, 48, 55, 56, 65

Offset: 1

Author

Reinhard Zumkeller, Nov 21 2011

Keywords

• nonn
• tabf
• look

Comments

A000292(n) = number of terms in row n;

T(1,1) = 3; right edge: T(n,A000292(n)) = A033428(n);

T(n,k) = T(n+1,k) for k <= A200738(n);

see table A200741 for distinct terms per row.

Examples

			First 5 rows:
1: 3;
2: 3,5,8,12;
3: 3,5,7,8,11,12,15,16,21,27;
4: 3,5,7,8,9,11,12,14,15,16,19,20,21,24,26,27,32,33,40,48;
5: 3,5,7,8,9,11,11,12,14,15,16,17,19,20,21,23,24,24,26,27,29,31,... .
First terms of 5th row:
T(5,1) = 1*1 + 1*1 + 1*1 = 3;
T(5,2) = 1*2 + 2*1 + 1*1 = 5;
T(5,3) = 1*3 + 3*1 + 1*1 = 7;
T(5,4) = 2*2 + 2*1 + 1*2 = 8;
T(5,5) = 1*4 + 4*1 + 1*1 = 9;
T(5,6) = 1*5 + 5*1 + 1*1 = 11;
T(5,7) = 2*3 + 3*1 + 1*2 = 11 = T(5,6);
T(5,8) = 2*2 + 2*2 + 2*2 = 12;
T(5,9) = 2*4 + 4*1 + 1*2 = 14;
T(5,10) = 3*3 + 3*1 + 1*3 = 15;
T(5,11) = 2*3 + 3*2 + 2*2 = 16;
T(5,12) = 2*5 + 5*1 + 1*2 = 17; ... .
		

Links

• Reinhard Zumkeller, Rows n=1..25 of triangle, flattened

Programs

Haskell

import Data.List (sort)
a200737 n k = a200737_tabl !! (n-1) !! (k-1)
a200737_row n = sort
   [v*w + w*u + u*v | w <- [1..n], v <- [1..w], u <- [1..v]]
a200737_tabl = map a200737_row [1..]