

A200737


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


5



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
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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 !! (n1) !! (k1)
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: A079965 A285069 A262736 * A200741 A271970 A213678
Adjacent sequences: A200734 A200735 A200736 * A200738 A200739 A200740


KEYWORD

nonn,tabf,look


AUTHOR

Reinhard Zumkeller, Nov 21 2011


STATUS

approved



