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

0,17

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.

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 *)

Prog

(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=', ')

Crossrefs

Cf. A000217, A002243, A033761.

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

Cf. A002636 (allows nondistinct triangular numbers).

Sequence in context: A329257 A173266 A342149 * A096496 A117209 A035192

Adjacent sequences: A224323 A224324 A224325 * A224327 A224328 A224329

Keyword

nonn

Author

Alex Ratushnyak, Apr 03 2013

Status

approved