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

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, 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, 43, 42, 37, 32, 26, 21, 15, 10, 6, 3, 1, 54, 53, 47, 41, 34, 28, 21, 15, 10, 6, 3, 1

Offset: 0

Author

N. J. A. Sloane

Keywords

• tabl
• nonn
• easy

Examples

			Triangle begins:
   1;
   2,1;
   4,3,1;
   7,6,3,1;
  10,9,6,3,1;
  ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10010 (rows 0 to 140, flattened)

Crossrefs

Cf. A027384, A027422.

Programs

Maple

f:= proc(n,k) local i,j;
   nops({seq(seq(i*j,j=i..n),i=k..n)})
end proc:
seq(seq(f(n,k),k=0..n),n=0..15); # Robert Israel, Apr 27 2025

Formula

From Robert Israel, Apr 27 2025: (Start)

T(n,n) = 1.

T(n,n-1) = 3 for n >= 2.

For each j, T(n,n-j) = (j+1)*(j+2)/2 for sufficiently large n. (End)

Extensions

More terms from Olivier Gérard, Nov 15 1997