A100438 Number of distinct products i*j*k*l for 1 <= i < j < k < l <= n.

0, 0, 0, 1, 5, 13, 29, 50, 79, 111, 186, 219, 345, 428, 513, 610, 884, 991, 1387, 1535, 1742, 1994, 2671, 2833, 3319, 3719, 4154, 4474, 5751, 5985, 7575, 8121, 8803, 9593, 10401, 10785, 13303, 14371, 15414, 15988, 19379, 20089, 24103, 25237, 26369

Offset: 1

Author

N. J. A. Sloane, Nov 21 2004

Keywords

• nonn

Crossrefs

Cf. A027425, A027430, A100435, A100436, A100437.

Programs

Maple

f:=proc(n) local i,j,k,l,t1; t1:={}; for i from 1 to n-3 do for j from i+1 to n-2 do for k from j+1 to n-1 do for l from k+1 to n do t1:={op(t1),i*j*k*l}; od: od: od: od: t1:=convert(t1,list); nops(t1); end;

Mathematica

f[n_] := Length[ Union[ Flatten[ Table[ i*j*k*l, {i, n}, {j, i + 1, n}, {k, j + 1, n}, {l, k + 1, n}]]]]; Table[ f[n], {n, 45}] (* Robert G. Wilson v, Dec 14 2004 *)

Python

def A100438(n): return len({i*j*k*l for i in range(1,n+1) for j in range(1,i) for k in range(1,j) for l in range(1,k)}) # Chai Wah Wu, Oct 16 2023

Extensions

More terms from Robert G. Wilson v, Dec 14 2004