A123068 Numbers represented by the "Little Methuselah" quadratic form x^2 + 2*y^2 + y*z + 4*z^2.

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

Offset

1,3

Comments

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.

References

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

Links

Table of n, a(n) for n=1..75.

Example

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+...

Prog

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

Crossrefs

Cf. A123063, A123064, A123065, A123067.

Sequence in context: A272323 A273881 A048266 * A247064 A160547 A348520

Adjacent sequences: A123065 A123066 A123067 * A123069 A123070 A123071

Keyword

nonn

Author

N. J. A. Sloane, Sep 27 2006

Status

approved