cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Nov 21 2004

Keywords

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

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

A102533 Number of distinct values of i*j + j*k + k*i with 1 <= i < j <= k <= n.

Original entry on oeis.org

0, 1, 4, 10, 20, 35, 50, 72, 100, 129, 163, 203, 244, 290, 346, 400, 461, 526, 600, 676, 756, 836, 925, 1018, 1117, 1220, 1325, 1435, 1554, 1683, 1811, 1938, 2078, 2212, 2367, 2526, 2677, 2835, 3003, 3169, 3350, 3527, 3714, 3898, 4099, 4304, 4498, 4713
Offset: 1

Views

Author

Robert G. Wilson v, Jan 13 2005

Keywords

Links

Crossrefs

Cf. A100439, A100440, A102534.

Programs

  • Maple
    F:= proc(n) local i,j;
      {seq(seq(i*j + (i+j)*n, i=1..j-1),j=2..n)}
end proc:
R:= NULL:
S:= {}:
for n from 1 to 50 do
  S:= S union F(n);
  R:= R, nops(S);
od:
R; # Robert Israel, Dec 15 2024
  • Mathematica
    f[n_] := Length[ Union[ Flatten[ Table[i*j + j*k + k*i, {i, n}, {j, i + 1, n}, {k, j, n}] ]]]; Table[ f[n], {n, 48}]

Extensions

Offset corrected by Robert Israel, Dec 15 2024

A102534 Number of distinct values of i*j + j*k + k*i with 1 <= i<= j < k <= n.

Original entry on oeis.org

0, 1, 4, 10, 19, 33, 49, 70, 96, 127, 161, 201, 238, 287, 337, 390, 449, 519, 586, 662, 741, 818, 902, 997, 1095, 1194, 1299, 1410, 1518, 1651, 1778, 1908, 2054, 2186, 2332, 2493, 2636, 2793, 2955, 3128, 3300, 3481, 3660, 3840, 4050, 4252, 4443, 4665, 4871
Offset: 1

Views

Author

Robert G. Wilson v, Jan 13 2005

Keywords

Links

Crossrefs

Cf. A100439, A100440, A102533.

Programs

  • Maple
    F:= proc(n) local i,j;
      {seq(seq(i*j + (i+j)*n, i=1..j),j=1..n-1)}
end proc:
R:= NULL:
S:= {}:
for n from 1 to 100 do
  S:= S union F(n);
  R:= R,nops(S);
od:
R; # Robert Israel, Dec 15 2024
  • Mathematica
    f[n_] := Length[ Union[ Flatten[ Table[i*j + j*k + k*i, {i, n}, {j, i, n}, {k, j + 1, n}]]]]; Table[ f[n], {n, 48}] (* Robert G. Wilson v, Jan 13 2005 *)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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