A027420 - OEIS

%I #16 Jun 15 2015 02:31:44

%S 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,

%T 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,

%U 37,43,36,25,15,6,1,6,15,25,36,43,54,42,31,20,10,3,3,10,20,31,42,54

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

%C T(n,0) = T(n,n) = A027384(n). - _Reinhard Zumkeller_, May 02 2014

%H Reinhard Zumkeller, <a href="/A027420/b027420.txt">Rows n = 0..125 of table, flattened</a>

%t 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 *)

%o (Haskell)

%o import Data.List (nub)

%o a027420 n k = a027420_tabl !! n !! k

%o a027420_row n = a027420_tabl !! n

%o a027420_tabl = zipWith (zipWith z) a002262_tabl a025581_tabl

%o                where z u v = length $ nub $ [i * j | i <- zs, j <- zs]

%o                              where zs = [min u v .. max u v]

%o -- _Reinhard Zumkeller_, May 02 2014

%Y Cf. A027384.

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

%K tabl,nonn,easy,nice

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Olivier Gérard_, Nov 15 1997