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%I #21 May 11 2021 11:54:33
%S 3,8,13,18,21,26,31,39,44,46,51,56,57,64,69,82,87,89,92,94,97,105,107,
%T 110,123,130,132,135,148,153,158,166,171,173,176,184,189,191,196,209,
%U 214,232,233,234,237,238,243,250,251,255,256,269,275,276,281,293,294
%N Sums of exactly three positive octahedral numbers A005900.
%D Dickson, L. E. History of the Theory of Numbers, Vol. 2: Diophantine Analysis. New York: Dover, 2005, cites the Pollock reference.
%D Pollock, F. "On the Extension of the Principle of Fermat's Theorem of the Polygonal Numbers to the Higher Orders of Series Whose Ultimate Differences Are Constant. With a New Theorem Proposed, Applicable to All the Orders." Abs. Papers Commun. Roy. Soc. London 5, 922-924, 1843-1850.
%H Agustin Moreno Canadas, <a href="http://arxiv.org/abs/0806.2486">On sums of figurate numbers by using techniques of poset representation theory</a>, arXiv:0806.2486 [math.NT], 2008.
%t lim = 300; oc[n_] := (2*n^3 + n)/3; nmax = Floor[Solve[oc[n] + oc[1] + oc[1] == lim, n][[1, 1, 2]]]; t = Table[ oc[n], {n, nmax}]; Select[ Union[ Flatten[ Outer[ Plus, t, t, t]]], # <= lim &] (* _Jean-François Alcover_, Sep 08 2011 *)
%Y Cf. A005900, A053676, A053677, A053678.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Oct 18 2007
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