A224326 Number of partitions of n into 3 distinct triangular numbers.

0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 2, 0, 1, 2, 0, 2, 2, 1, 1, 2, 1, 1, 3, 2, 0, 2, 1, 1, 4, 1, 3, 1, 1, 2, 2, 2, 1, 4, 1, 1, 4, 1, 2, 4, 1, 2, 2, 2, 2, 3, 2, 2, 4, 1, 2, 3, 2, 3, 4, 1, 2, 4, 2, 3, 3, 2, 1, 5, 2, 0, 5, 1, 4, 5, 2, 4, 2, 2

Offset: 0

Author

Alex Ratushnyak, Apr 03 2013

Keywords

• nonn

Comments

Indices of zeros: 0 followed by A002243.

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000
• Jon Maiga, Computer-generated formulas for A224326, Sequence Machine.

Crossrefs

Cf. A000217, A002243, A033761.

Cf. A025436 (number of partitions of n into 3 distinct squares).

Cf. A002636 (allows nondistinct triangular numbers).

Programs

Mathematica

nn = 150; tri = Table[n*(n + 1)/2, {n, 0, nn}]; t = Table[0, {tri[[-1]]}]; Do[s = tri[[i]] + tri[[j]] + tri[[k]]; If[s <= tri[[-1]], t[[s]]++], {i, nn}, {j, i + 1, nn}, {k, j + 1, nn}]; t = Join[{0}, t] (* T. D. Noe, Apr 05 2013 *)

Python

TOP = 777
for n in range(TOP):
  k = 0
  for x in range(TOP):
    s = x*(x+1)//2
    if s>n: break
    for y in range(x+1,TOP):
        sy = s + y*(y+1)//2
        if sy>n: break
        for z in range(y+1,TOP):
          sz = sy + z*(z+1)//2
          if sz>n: break
          if sz==n: k+=1
  print(str(k), end=',')