A100440 Number of distinct values of i*j + j*k + k*i with 1 <= i <= j <= k <= n.

1, 4, 10, 20, 33, 50, 68, 93, 123, 154, 193, 233, 276, 325, 377, 434, 500, 568, 643, 720, 804, 885, 979, 1068, 1168, 1274, 1381, 1495, 1615, 1746, 1876, 2005, 2148, 2285, 2437, 2596, 2748, 2908, 3077, 3241, 3425, 3608, 3796, 3979, 4181, 4388, 4585, 4804, 5015, 5237

Offset: 1

Author

N. J. A. Sloane, Nov 21 2004

Keywords

• nonn

Comments

a(n) <= A000292(n); a(n) = number of terms in n-th row of the triangle in A200741. - Reinhard Zumkeller, Nov 21 2011

Links

• David A. Corneth, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A027430, A100439, A102533, A102534, A200737.

Programs

Haskell

a100440 = length . a200741_row  -- Reinhard Zumkeller, Nov 21 2011

Maple

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

Mathematica

f[n_] := Length[ Union[ Flatten[ Table[i*j + j*k + k*i, {i, n}, {j, i, n}, {k, j, n}] ]]]; Table[ f[n], {n, 48}] (* Robert G. Wilson v, Dec 14 2004 *)

PARI

first(n) = {my(v = vector(3*n^2, i, oo), res = vector(n)); forvec(x = vector(3, i, [1,n]), c = x[1]*x[2] + x[1]*x[3] + x[2]*x[3]; v[c] = min(x[3],v[c]); , 1); for(i = 1, #v, if(v[i] < oo, res[v[i]]++)); for(i = 2, #res, res[i] += res[i-1]); res } \\ David A. Corneth, Mar 23 2021

Python

from numba import njit
@njit()
def aupton(terms):
  aset, alst = set(), []
  for n in range(1, terms+1):
    for i in range(1, n+1):
      for j in range(i, n+1):
        aset.add(i*j + j*n + n*i)
    alst.append(len(aset))
  return alst
print(aupton(50)) # Michael S. Branicky, Mar 23 2021

Extensions

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