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A224326
Number of partitions of n into 3 distinct triangular numbers.
2
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
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. 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
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Apr 03 2013
STATUS
approved