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%I #5 Jul 20 2012 21:28:29
%S 3,5,7,8,9,10,13,14,15,16,18,24,25,36,38,50,53,55,60,69,81,83,99,110,
%T 119
%N Numbers having a unique partition into three positive triangular numbers.
%C A063993(a(n)) = 1. - _Reinhard Zumkeller_, Jul 20 2012
%e Example: 119=55+36+28
%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, 1, lim}, {b, a, trigInv[trig[lim]-trig[a]]}, {c, b, trigInv[trig[lim]-trig[a]-trig[b]]}]; Flatten[Position[nLst, 1]]
%Y Cf. A060773 (n having a unique partition into three nonnegative triangular numbers).
%Y Cf. A002097, A064825.
%K fini,full,nonn
%O 1,1
%A _T. D. Noe_, Aug 10 2005