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

1,1

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.

Links

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

Example

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; ... .

Prog

(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..]

Crossrefs

Sequence in context: A262736 A318684 A336132 * A200741 A271970 A213678

Adjacent sequences: A200734 A200735 A200736 * A200738 A200739 A200740

Keyword

nonn,tabf,look

Author

Reinhard Zumkeller, Nov 21 2011

Status

approved