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A027421 Triangle T(n,k) = number of distinct products i*j with k<=i,j<=n, for 0<=k<=n.

%I A027421 #17 Jul 08 2025 17:51:52
%S A027421 1,2,1,4,3,1,7,6,3,1,10,9,6,3,1,15,14,10,6,3,1,19,18,14,10,6,3,1,26,
%T A027421 25,20,15,10,6,3,1,31,30,25,20,15,10,6,3,1,37,36,31,26,20,15,10,6,3,1,
%U A027421 43,42,37,32,26,21,15,10,6,3,1,54,53,47,41,34,28,21,15,10,6,3,1
%N A027421 Triangle T(n,k) = number of distinct products i*j with k<=i,j<=n, for 0<=k<=n.
%H A027421 Robert Israel, <a href="/A027421/b027421.txt">Table of n, a(n) for n = 0..10010</a> (rows 0 to 140, flattened)
%F A027421 From _Robert Israel_, Apr 27 2025: (Start)
%F A027421 T(n,n) = 1.
%F A027421 T(n,n-1) = 3 for n >= 2.
%F A027421 For each j, T(n,n-j) = (j+1)*(j+2)/2 for sufficiently large n. (End)
%e A027421 Triangle begins:
%e A027421    1;
%e A027421    2,1;
%e A027421    4,3,1;
%e A027421    7,6,3,1;
%e A027421   10,9,6,3,1;
%e A027421   ...
%p A027421 f:= proc(n,k) local i,j;
%p A027421    nops({seq(seq(i*j,j=i..n),i=k..n)})
%p A027421 end proc:
%p A027421 seq(seq(f(n,k),k=0..n),n=0..15); # _Robert Israel_, Apr 27 2025
%Y A027421 Cf. A027384, A027422.
%K A027421 tabl,nonn,easy
%O A027421 0,2
%A A027421 _N. J. A. Sloane_
%E A027421 More terms from _Olivier Gérard_, Nov 15 1997