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

%I A224326 #24 Feb 07 2022 20:18:31
%S A224326 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,
%T A224326 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,
%U A224326 1,2,4,2,3,3,2,1,5,2,0,5,1,4,5,2,4,2,2
%N A224326 Number of partitions of n into 3 distinct triangular numbers.
%C A224326 Indices of zeros: 0 followed by A002243.
%H A224326 T. D. Noe, <a href="/A224326/b224326.txt">Table of n, a(n) for n = 0..10000</a>
%H A224326 Jon Maiga, <a href="http://sequencedb.net/s/A224326">Computer-generated formulas for A224326</a>, Sequence Machine.
%t A224326 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 *)
%o A224326 (Python)
%o A224326 TOP = 777
%o A224326 for n in range(TOP):
%o A224326   k = 0
%o A224326   for x in range(TOP):
%o A224326     s = x*(x+1)//2
%o A224326     if s>n: break
%o A224326     for y in range(x+1,TOP):
%o A224326         sy = s + y*(y+1)//2
%o A224326         if sy>n: break
%o A224326         for z in range(y+1,TOP):
%o A224326           sz = sy + z*(z+1)//2
%o A224326           if sz>n: break
%o A224326           if sz==n: k+=1
%o A224326   print(str(k), end=',')
%Y A224326 Cf. A000217, A002243, A033761.
%Y A224326 Cf. A025436 (number of partitions of n into 3 distinct squares).
%Y A224326 Cf. A002636 (allows nondistinct triangular numbers).
%K A224326 nonn
%O A224326 0,17
%A A224326 _Alex Ratushnyak_, Apr 03 2013