A133330 Sums of exactly three positive octahedral numbers A005900.

3, 8, 13, 18, 21, 26, 31, 39, 44, 46, 51, 56, 57, 64, 69, 82, 87, 89, 92, 94, 97, 105, 107, 110, 123, 130, 132, 135, 148, 153, 158, 166, 171, 173, 176, 184, 189, 191, 196, 209, 214, 232, 233, 234, 237, 238, 243, 250, 251, 255, 256, 269, 275, 276, 281, 293, 294

Offset: 1

Author

Jonathan Vos Post, Oct 18 2007

Keywords

• easy
• nonn

References

• Dickson, L. E. History of the Theory of Numbers, Vol. 2: Diophantine Analysis. New York: Dover, 2005, cites the Pollock reference.
• 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.

Links

• Agustin Moreno Canadas, On sums of figurate numbers by using techniques of poset representation theory, arXiv:0806.2486 [math.NT], 2008.

Crossrefs

Cf. A005900, A053676, A053677, A053678.

Programs

Mathematica

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 *)