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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 3 01:46 EST 2023. Contains 360024 sequences. (Running on oeis4.)