A027420 Triangle T00, T10, T01, T20, T11, T02, etc., where Tmn = number of distinct products ij with min(m,n) <= i,j <= max(m,n).

1, 2, 2, 4, 1, 4, 7, 3, 3, 7, 10, 6, 1, 6, 10, 15, 9, 3, 3, 9, 15, 19, 14, 6, 1, 6, 14, 19, 26, 18, 10, 3, 3, 10, 18, 26, 31, 25, 14, 6, 1, 6, 14, 25, 31, 37, 30, 20, 10, 3, 3, 10, 20, 30, 37, 43, 36, 25, 15, 6, 1, 6, 15, 25, 36, 43, 54, 42, 31, 20, 10, 3, 3, 10, 20, 31, 42, 54

Offset: 0

Author

N. J. A. Sloane

Keywords

• tabl
• nonn
• easy
• nice

Comments

T(n,0) = T(n,n) = A027384(n). - Reinhard Zumkeller, May 02 2014

Links

• Reinhard Zumkeller, Rows n = 0..125 of table, flattened

Crossrefs

Cf. A027384.

Cf. A241944 (row sums), A002262, A025581.

Programs

Haskell

import Data.List (nub)
a027420 n k = a027420_tabl !! n !! k
a027420_row n = a027420_tabl !! n
a027420_tabl = zipWith (zipWith z) a002262_tabl a025581_tabl
               where z u v = length $ nub $ [i * j | i <- zs, j <- zs]
                             where zs = [min u v .. max u v]
-- Reinhard Zumkeller, May 02 2014

Mathematica

t[m_, n_] := i*j /. {ToRules @ Reduce[ Min[m, n] <= i <= j <= Max[m, n], Integers]} // Union // Length; row[n_] := Table[ t[m, n-m], {m, 0, n} ]; Table[ row[n], {n, 0, 11}] // Flatten (* Jean-François Alcover, Apr 16 2013 *)

Extensions

More terms from Olivier Gérard, Nov 15 1997