%I #8 Sep 08 2022 08:45:28

%S 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,

%T 26,27,28,29,30,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,

%U 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75

%N Numbers represented by the "Little Methuselah" quadratic form x^2 + 2*y^2 + y*z + 4*z^2.

%C Theorem (Conway, p. 81) This ternary form represents every number from 0 to 32 except 31. Any other integer-valued ternary form not equivalent to this one fails to represent some number between 1 and 30.

%D J. H. Conway, The Sensual (Quadratic) Form, M.A.A., 1997, p. 82.

%e 1+2*x+2*x^2+4*x^3+4*x^4+6*x^5+8*x^6+2*x^7+10*x^8+10*x^9+2*x^10+...

%o (Magma) L:=LatticeWithGram(3, [2,0,0,0,4,1,0,1,8] ); T<q> := ThetaSeries(L,500); T;

%Y Cf. A123063, A123064, A123065, A123067.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Sep 27 2006