%I A118278
%S A118278 0,1,33066,146858,273118,1,1274522,2117145,3613278,1,7250758,1,12911636,
%T A118278 1,22655394,26801303,25049533,1,56922533
%V A118278 0,-1,33066,146858,273118,-1,1274522,2117145,3613278,-1,7250758,-1,12911636,
               -1,
%W A118278 22655394,26801303,25049533,-1,56922533
%N A118278 Conjectured largest number that is not the sum of three n-gonal numbers, 
               or -1 if there is no largest number.
%C A118278 Extensive calculations show that if a(n)>=0, then every number greater 
               than a(n) can be represented as the sum of three n-gonal numbers. 
               a(3)=0 because every number can be written as the sum of three triangular 
               numbers. When n is a multiple of 4, there is an infinite set of numbers 
               not representable. For n=14, there appears to be a sparse, but infinite, 
               set of numbers not representable.
%D A118278 R. K. Guy, Every number is expressible as the sum of how many polygonal 
               numbers?, Amer. Math. Monthly 101 (1994), 169-172.
%H A118278 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PolygonalNumber.html">MathWorld: Polygonal Number</a>
%Y A118278 Cf. A118279 (number of numbers not representable), A003679 (not the sum 
               of three pentaagonal numbers), A007536 (not the sum of three hexagonal 
               numbers).
%Y A118278 Sequence in context: A045061 A132992 A153748 this_sequence A118280 A062682 
               A094889
%Y A118278 Adjacent sequences: A118275 A118276 A118277 this_sequence A118279 A118280 
               A118281
%K A118278 sign
%O A118278 3,3
%A A118278 T. D. Noe (noe(AT)sspectra.com), Apr 21 2006