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A131280 Sums of exactly 4 positive octahedral numbers A005900.

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%I A131280 #5 Nov 26 2013 20:29:28
%S A131280 4,9,14,19,22,24,27,32,37,40,45,47,50,52,57,58,62,63,65,70,75,76,83,
%T A131280 88,90,93,95,98,100,101,103,106,108,111,113,116,124,126,129,131,133,
%U A131280 136,138,141,142,149,151,154,159,164,167,172,174,176,177,179,182,185,190
%N A131280 Sums of exactly 4 positive octahedral numbers A005900.
%C A131280 Pollock (1850) conjectured that every number is the sum of at most 7 octahedral numbers. Which octahedral numbers are themselves the sum of exactly 4 positive octahedral numbers? To begin with, Oc(3) = Oc(2) + Oc(2) + Oc(2) + Oc(1) = 6 + 6 + 6 + 1 = 19.
%D A131280 Dickson, L. E. History of the Theory of Numbers, Vol. 2: Diophantine Analysis. New York: Dover, 2005, cites the Pollock reference.
%D A131280 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.
%t A131280 With[{octs=Table[(2n^3+n)/3,{n,10}]},Take[Union[Total/@Tuples[octs,4]], 60]] (* _Harvey P. Dale_, Nov 26 2013 *)
%Y A131280 Cf. A005900, A053676-A053678, A133330.
%K A131280 easy,nonn
%O A131280 1,1
%A A131280 _Jonathan Vos Post_, Oct 21 2007