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%I #5 Mar 31 2012 10:26:35
%S 0,1,2,4,5,8,11,14,20,29,50,53
%N Numbers having a unique partition into three nonnegative triangular numbers.
%t trig[n_]:=n(n+1)/2; trigInv[x_]:=Ceiling[Sqrt[Max[0, 2x]]]; lim=100; nLst=Table[0, {trig[lim]}]; Do[n=trig[a]+trig[b]+trig[c]; If[n>0 && n<=trig[lim], nLst[[n]]++ ], {a, 0, lim}, {b, a, trigInv[trig[lim]-trig[a]]}, {c, b, trigInv[trig[lim]-trig[a]-trig[b]]}]; Flatten[Position[nLst, 1]] (_T. D. Noe_, Aug 10 2005)
%Y Cf. A000217, A061262, A053614.
%Y Cf. A111638 (n having a unique partition into three positive triangular numbers).
%K nonn,fini,full
%O 0,3
%A _Erich Friedman_, Apr 24 2001
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